diff --git a/lib/WeBWorK/PG/Translator.pm b/lib/WeBWorK/PG/Translator.pm
index 50a38f126..2c195ad78 100644
--- a/lib/WeBWorK/PG/Translator.pm
+++ b/lib/WeBWorK/PG/Translator.pm
@@ -1088,46 +1088,71 @@ sub rf_avg_problem_grader {
 }
 
 sub avg_problem_grader {
-	my ($rh_evaluated_answers, $rh_problem_state, %form_options) = @_;
+	my ($answers, $problem_state, %form_options) = @_;
 
-	my %evaluated_answers = %{$rh_evaluated_answers};
+	my %problem_result = (score => 0, errors => '', type => 'avg_problem_grader', msg => '');
 
-	# By default the old problem state is simply passed back out again.
-	my %problem_state = %$rh_problem_state;
+	$problem_result{msg} = maketext('You can earn partial credit on this problem.') if keys %$answers > 1;
 
-	# Initial setup of the answer
-	my $total          = 0;
-	my %problem_result = (
-		score  => 0,
-		errors => '',
-		type   => 'avg_problem_grader',
-		msg    => '',
-	);
+	# Return unless answers have been submitted.
+	return (\%problem_result, $problem_state) unless $form_options{answers_submitted} == 1;
+
+	my %credit;
+
+	# Get the score for each answer (error if can't recognize the answer format).
+	for my $ans_name (keys %$answers) {
+		if (ref($answers->{$ans_name}) =~ m/^(HASH|AnswerHash)$/) {
+			$credit{$ans_name} = $answers->{$ans_name}{score} // 0;
+		} else {
+			$problem_result{error} = "Error: Answer $ans_name is not a hash: $answers->{$ans_name}";
+			die "Error: Answer |$ans_name| is not a hash reference\n"
+				. $answers->{$ans_name}
+				. "\nThis probably means that the answer evaluator for this answer is not working correctly.";
+		}
+	}
 
-	my $count = keys %evaluated_answers;
-	$problem_result{msg} = 'You can earn partial credit on this problem.' if $count > 1;
+	# Mark any optional answers as correct, if the goal answers are right and the optional answers are blank.
+	for my $ans_name (keys %$answers) {
+		if ($credit{$ans_name} == 1 && defined $answers->{$ans_name}{credit}) {
+			for my $credit_name (
+				ref($answers->{$ans_name}{credit}) eq 'ARRAY'
+				? @{ $answers->{$ans_name}{credit} }
+				: $answers->{$ans_name}{credit})
+			{
+				if (!defined $answers->{$credit_name}{student_ans}
+					|| $answers->{$credit_name}{student_ans} =~ m/^\s*$/)
+				{
+					$answers->{$credit_name}{score} = 1;
+					$answers->{$credit_name}{ans_message} =
+						maketext('This answer was marked correct because the primary answer is correct.');
+					$credit{$credit_name} = 1;
+				}
+			}
+		}
+	}
 
-	return (\%problem_result, \%problem_state) unless $form_options{answers_submitted} == 1;
+	my ($score, $total) = (0, 0);
 
-	# Answers have been submitted -- process them.
-	for my $ans_name (keys %evaluated_answers) {
-		$total += $evaluated_answers{$ans_name}{score};
+	# Add up the weighted scores
+	for my $ans_name (keys %$answers) {
+		my $weight = $answers->{$ans_name}{weight} // 1;
+		$total += $weight;
+		$score += $weight * $credit{$ans_name};
 	}
 
-	# Calculate score rounded to three places to avoid roundoff problems
-	$problem_result{score} = $count ? $total / $count : 0;
-	$problem_state{recorded_score} //= 0;
+	$problem_result{score} = $total ? $score / $total : 0;
 
-	# Increase recorded score if the current score is greater.
-	$problem_state{recorded_score} = $problem_result{score}
-		if $problem_result{score} > $problem_state{recorded_score};
+	++$problem_state->{num_of_correct_ans}   if $score == $total;
+	++$problem_state->{num_of_incorrect_ans} if $score < $total;
+	$problem_state->{recorded_score} //= 0;
 
-	++$problem_state{num_of_correct_ans}   if $total == $count;
-	++$problem_state{num_of_incorrect_ans} if $total < $count;
+	# Increase recorded score if the current score is greater.
+	$problem_state->{recorded_score} = $problem_result{score}
+		if $problem_result{score} > $problem_state->{recorded_score};
 
-	warn "Error in grading this problem the total $total is larger than $count" if $total > $count;
+	warn "Error in grading this problem: The score $score is larger than the total $total." if $score > $total;
 
-	return (\%problem_result, \%problem_state);
+	return (\%problem_result, $problem_state);
 }
 
 =head2 post_process_content
diff --git a/macros/core/PGanswermacros.pl b/macros/core/PGanswermacros.pl
index c2dbb469b..9e9a0bd05 100644
--- a/macros/core/PGanswermacros.pl
+++ b/macros/core/PGanswermacros.pl
@@ -1587,62 +1587,142 @@ sub std_problem_grader2 {
 
 =head3 C<avg_problem_grader>
 
-This grader gives a grade depending on how many questions from the problem are correct.  (The highest
-grade is the one that is kept.  One can never lower the recorded grade on a problem by repeating it.)
-Many professors (and almost all students :-) ) prefer this grader.
+This grader gives a "weighted" average score to the problem and is the default
+grader.
+
+The grader can be selected by calling
 
     install_problem_grader(~~&avg_problem_grader);
 
+However, since this is the default grader, that is not necessary to use this
+grader.
+
+Each answer is assigned a weight (the default is 1). The score is then the sum
+of the product of the weights and scores for the correct answers divided by the
+total of the weights for all answers. (To assign weights as percentages, use
+integers that add up to 100. For example, use 40 and 60 for the weights for two
+answers.) Assign weights to answers using the C<cmp> option C<< weight => n >>.
+For example, in PGML create the answer rule with
+
+    [_]{$answer}{10}{ cmp_options => { weight => 40 } }
+
+With the classic C<ANS> method call
+
+    ANS($answer->cmp(weight => 40);
+
+This grader also allows for one "goal" answer that is answered correctly to
+automatically give credit for one or more other "optional" answers. This way, if
+there are several "optional" answers leading up to the "goal" answer, and the
+student produces the "goal" answer by some other means and does not answer the
+"optional" answers, the student can be given full credit for the problem anyway.
+To use this feature use the C<credit> option of the C<cmp> method for the "goal"
+answer. For example, C<< credit => $answer1Name >> or C<< credit => [
+$answer1Name, $answer2Name, ... ] >>, where C<$answer1Name>, C<$answer2Name>,
+etc., are the names of the "optional" answers that will be given credit if the
+"goal" answer is correct. Note that the other answers must be assigned names
+either by calling C<NAMED_ANS_RULE> and C<NAMED_ANS>, or by creating the answer
+rule in PGML with C<[_]{$answer1}{15}{$answer1Name}>, for example. The answer
+names should be generated by calling C<NEW_ANS_NAME> (for example,
+C<$answer1Name = NEW_ANS_NAME()>) rather than being made up.  Otherwise the
+problem will fail to work in many situations (for example, in tests). For
+example, to set this up in PGML use
+
+    BEGIN_PGML
+    Optional Answer 1: [_]{$answer1}{10}{$answer1Name = NEW_ANS_NAME()}
+
+    Optional Answer 2: [_]{$answer2}{10}{$answer2Name = NEW_ANS_NAME()}
+
+    Goal: [_]{$answer3}{10}{ cmp_options => { credit => [ $answer1Name, $answer2Name ] } }
+    END_PGML
+
+Note that the C<credit> and C<weight> options can be used together. For example:
+
+    BEING_PGML
+    Optional Answer: [_]{$optional}{10}{$optionalName = NEW_ANS_NAME()}{{ weight => 20 }}
+
+    Goal: [_]{$goalAnswer}{10}{ cmp_options => { credit => $optionalName, weight => 80 } }
+    END_PGML
+
+This way, if the "optional" answer is correct but the "goal" answer is not, the
+problem score will be 20%, but if the "goal" answer is correct, the problem
+score will be 100%.
+
+One caveat to keep in mind is that credit is given to an "optional" answer ONLY
+if the answer is left blank (or is actually correct). Credit will NOT be given
+if an "optional" answer is incorrect, even if the "goal" answer IS correct.
+
+When credit is given to an "optional" answer due to the "goal" answer being
+correct, a message will be added to the "optional" answer stating, "This answer
+was marked correct because the primary answer is correct."
+
 =cut
 
 sub avg_problem_grader {
-	my ($rh_evaluated_answers, $rh_problem_state, %form_options) = @_;
+	my ($answers, $problem_state, %form_options) = @_;
 
-	my %evaluated_answers = %{$rh_evaluated_answers};
+	my %problem_result = (score => 0, errors => '', type => 'avg_problem_grader', msg => '');
 
-	# By default the old problem state is simply passed back out again.
-	my %problem_state = %$rh_problem_state;
-
-	# Initial setup of the answer.
-	my $total          = 0;
-	my %problem_result = (
-		score  => 0,
-		errors => '',
-		type   => 'avg_problem_grader',
-		msg    => '',
-	);
-	my $count = keys %evaluated_answers;
-	$problem_result{msg} = maketext('You can earn partial credit on this problem.') if $count > 1;
+	$problem_result{msg} = maketext('You can earn partial credit on this problem.') if keys %$answers > 1;
 
 	# Return unless answers have been submitted.
-	return (\%problem_result, \%problem_state) unless $form_options{answers_submitted} == 1;
+	return (\%problem_result, $problem_state) unless $form_options{answers_submitted} == 1;
 
-	# Answers have been submitted -- process them.
-	for my $ans_name (keys %evaluated_answers) {
-		if (ref $evaluated_answers{$ans_name} eq 'HASH' || ref $evaluated_answers{$ans_name} eq 'AnswerHash') {
-			$total += $evaluated_answers{$ans_name}{score} // 0;
+	my %credit;
+
+	# Get the score for each answer (error if can't recognize the answer format).
+	for my $ans_name (keys %$answers) {
+		if (ref($answers->{$ans_name}) =~ m/^(HASH|AnswerHash)$/) {
+			$credit{$ans_name} = $answers->{$ans_name}{score} // 0;
 		} else {
+			$problem_result{error} = "Error: Answer $ans_name is not a hash: $answers->{$ans_name}";
 			die "Error: Answer |$ans_name| is not a hash reference\n"
-				. $evaluated_answers{$ans_name}
-				. 'This probably means that the answer evaluator for this answer is not working correctly.';
-			$problem_result{error} = "Error: Answer $ans_name is not a hash: $evaluated_answers{$ans_name}";
+				. $answers->{$ans_name}
+				. "\nThis probably means that the answer evaluator for this answer is not working correctly.";
 		}
 	}
 
-	# Calculate the score.
-	$problem_result{score} = $total / $count if $count;
+	# Mark any optional answers as correct, if the goal answers are right and the optional answers are blank.
+	for my $ans_name (keys %$answers) {
+		if ($credit{$ans_name} == 1 && defined $answers->{$ans_name}{credit}) {
+			for my $credit_name (
+				ref($answers->{$ans_name}{credit}) eq 'ARRAY'
+				? @{ $answers->{$ans_name}{credit} }
+				: $answers->{$ans_name}{credit})
+			{
+				if (!defined $answers->{$credit_name}{student_ans}
+					|| $answers->{$credit_name}{student_ans} =~ m/^\s*$/)
+				{
+					$answers->{$credit_name}{score} = 1;
+					$answers->{$credit_name}{ans_message} =
+						maketext('This answer was marked correct because the primary answer is correct.');
+					$credit{$credit_name} = 1;
+				}
+			}
+		}
+	}
 
-	++$problem_state{num_of_correct_ans}   if $total == $count;
-	++$problem_state{num_of_incorrect_ans} if $total < $count;
-	$problem_state{recorded_score} //= 0;
+	my ($score, $total) = (0, 0);
+
+	# Add up the weighted scores
+	for my $ans_name (keys %$answers) {
+		my $weight = $answers->{$ans_name}{weight} // 1;
+		$total += $weight;
+		$score += $weight * $credit{$ans_name};
+	}
+
+	$problem_result{score} = $total ? $score / $total : 0;
+
+	++$problem_state->{num_of_correct_ans}   if $score == $total;
+	++$problem_state->{num_of_incorrect_ans} if $score < $total;
+	$problem_state->{recorded_score} //= 0;
 
 	# Increase recorded score if the current score is greater.
-	$problem_state{recorded_score} = $problem_result{score}
-		if $problem_result{score} > $problem_state{recorded_score};
+	$problem_state->{recorded_score} = $problem_result{score}
+		if $problem_result{score} > $problem_state->{recorded_score};
 
-	warn "Error in grading this problem the total $total is larger than $count" if $total > $count;
+	warn "Error in grading this problem: The score $score is larger than the total $total." if $score > $total;
 
-	return (\%problem_result, \%problem_state);
+	return (\%problem_result, $problem_state);
 }
 
 =head2 Utility subroutines