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13 Jan 2026, 12:32
Kudos
Bookmarks
Alex Total: 240
Afternoon Total: 180
A team composed of Alex and Maya sold souvenir booklets at two performances of a local orchestra on the same day: one performance took place in the afternoon and the other took place in the evening. Each booklet sold for $4 at the afternoon performance and $6 at the evening performance. Alex sold twice as many booklets in the afternoon performance as Maya sold in the evening performance, and Maya sold half as many booklets in the afternoon performance as Alex sold in the evening performance. Altogether, the team earned $1,800 from booklet sales that day.
In the table, select for Alex Total the total number of booklets Alex sold that day and select for Afternoon Total the total number of booklets the team sold at the afternoon performance that would be jointly consistent with the given information. Make only two selections, one in each column.
In the table, select for Alex Total the total number of booklets Alex sold that day and select for Afternoon Total the total number of booklets the team sold at the afternoon performance that would be jointly consistent with the given information. Make only two selections, one in each column.
| Alex Total | Afternoon Total | |
| 120 | ||
| 180 | ||
| 240 | ||
| 260 | ||
| 300 |
ShowHide Answer
Official Answer
Alex Total: 240
Afternoon Total: 180
13 Jan 2026, 12:32
Kudos
Bookmarks
Official Solution:
Let:
\(a =\) Alex's afternoon sales
\(b =\) Alex's evening sales
\(c =\) Maya's afternoon sales
\(d =\) Maya's evening sales
Given:
\(a = 2d\)
\(c = \frac{b}{2}\), so \(b = 2c\).
Total revenue:
\(4(a + c) + 6(b + d) = 1800\)
Substitute:
\(4(2d + c) + 6(2c + d) = 1800\)
\(7d + 8c = 900\)
• The total number of booklets Alex sold that day = \(a + b = 2d + 2c = 2(d + c)\)
• The total number of booklets the team sold on the afternoon = \(a + c = 2d + c\)
Now, let's test the options and verify against \(7d + 8c = 900\).
• If Alex Total is 120, then \(2(d + c) = 120\), which gives \(d + c = 60\). Multiply by 8: \(8d + 8c = 480\). Subtract \(7d + 8c = 900\) from it to get \(d = -420\). Since d cannot be negative, discard this option for Alex Total.
• If Alex Total is 180, then \(2(d + c) = 180\), which gives \(d + c = 90\). Multiply by 8: \(8d + 8c = 720\). Subtract \(7d + 8c = 900\) from it to get \(d = -180\). Since d cannot be negative, discard this option for Alex Total.
• If Alex Total is 240, then \(2(d + c) = 240\), which gives \(d + c = 120\). Multiply by 8: \(8d + 8c = 960\). Subtract \(7d + 8c = 900\) from it to get \(d = 60\). Then, from \(d + c = 120\), we get \(c = 60\). This fits!
Thus:
• The total number of booklets Alex sold that day = \(a + b = 2d + 2c = 2(d + c) = 240\).
• The total number of booklets the team sold on the afternoon = \(a + c = 2d + c = 180\).
Correct answer:
Alex Total "240"
Afternoon Total "180"
Bunuel
Let:
\(a =\) Alex's afternoon sales
\(b =\) Alex's evening sales
\(c =\) Maya's afternoon sales
\(d =\) Maya's evening sales
Given:
\(a = 2d\)
\(c = \frac{b}{2}\), so \(b = 2c\).
Total revenue:
\(4(a + c) + 6(b + d) = 1800\)
Substitute:
\(4(2d + c) + 6(2c + d) = 1800\)
\(7d + 8c = 900\)
• The total number of booklets Alex sold that day = \(a + b = 2d + 2c = 2(d + c)\)
• The total number of booklets the team sold on the afternoon = \(a + c = 2d + c\)
Now, let's test the options and verify against \(7d + 8c = 900\).
• If Alex Total is 120, then \(2(d + c) = 120\), which gives \(d + c = 60\). Multiply by 8: \(8d + 8c = 480\). Subtract \(7d + 8c = 900\) from it to get \(d = -420\). Since d cannot be negative, discard this option for Alex Total.
• If Alex Total is 180, then \(2(d + c) = 180\), which gives \(d + c = 90\). Multiply by 8: \(8d + 8c = 720\). Subtract \(7d + 8c = 900\) from it to get \(d = -180\). Since d cannot be negative, discard this option for Alex Total.
• If Alex Total is 240, then \(2(d + c) = 240\), which gives \(d + c = 120\). Multiply by 8: \(8d + 8c = 960\). Subtract \(7d + 8c = 900\) from it to get \(d = 60\). Then, from \(d + c = 120\), we get \(c = 60\). This fits!
Thus:
• The total number of booklets Alex sold that day = \(a + b = 2d + 2c = 2(d + c) = 240\).
• The total number of booklets the team sold on the afternoon = \(a + c = 2d + c = 180\).
Correct answer:
Alex Total "240"
Afternoon Total "180"
