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07 Aug 2026, 11:41
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Container 1: 72
Container 2: 64
Clara was assembling display trays using gold, green, and white beads from two containers.
• In Container 1, the ratio of gold beads to green beads to white beads was \(1:3:2\).
• In Container 2, the ratio of gold beads to green beads to white beads was \(4:1:3\).
Across the two containers combined, the total number of gold beads was equal to the total number of green beads.
Select for Container 1 the possible total number of beads in Container 1, and select for Container 2 the possible total number of beads in Container 2, that would be jointly consistent with the given information. Make only two selections, one in each column.
• In Container 1, the ratio of gold beads to green beads to white beads was \(1:3:2\).
• In Container 2, the ratio of gold beads to green beads to white beads was \(4:1:3\).
Across the two containers combined, the total number of gold beads was equal to the total number of green beads.
Select for Container 1 the possible total number of beads in Container 1, and select for Container 2 the possible total number of beads in Container 2, that would be jointly consistent with the given information. Make only two selections, one in each column.
| Container 1 | Container 2 | |
| 40 | ||
| 45 | ||
| 54 | ||
| 64 | ||
| 72 | ||
| 81 |
ShowHide Answer
Official Answer
Container 1: 72
Container 2: 64
07 Aug 2026, 11:41
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Official Solution:
In Container 1, the ratio of gold beads to green beads to white beads is \(1:3:2\). So:
• Gold \(= x\)
• Green \(= 3x\)
• White \(= 2x\)
Total \(= 6x\)
In Container 2, the ratio of gold beads to green beads to white beads is \(4:1:3\). So:
• Gold \(= 4y\)
• Green \(= y\)
• White \(= 3y\)
Total \(= 8y\)
Across the two containers combined, the number of gold beads equals the number of green beads. So:
\(x + 4y = 3x + y\)
\(3y = 2x\)
\(x = \frac{3y}{2}\)
So the total number of beads in Container 1 is:
\(6x = 6 * \frac{3y}{2} = 9y\)
The total number of beads in Container 2 is:
\(8y\)
Therefore, the totals in Container 1 and Container 2 must be in the ratio \(9:8\). Check the options for a \(9:8\) ratio pair.
• The pair 45 and 40 has the ratio \(9:8\), but 45 cannot be the total for Container 1 because Container 1’s total must be a multiple of 6.
• The pair 72 and 64 has the ratio \(9:8\), and 72 is a multiple of 6 while 64 is a multiple of 8.
• The pair 81 and 72 has the ratio \(9:8\), but 81 cannot be the total for Container 1 because Container 1’s total must be a multiple of 6.
Correct answer:
Container 1 "72"
Container 2 "64"
Bunuel
In Container 1, the ratio of gold beads to green beads to white beads is \(1:3:2\). So:
• Gold \(= x\)
• Green \(= 3x\)
• White \(= 2x\)
Total \(= 6x\)
In Container 2, the ratio of gold beads to green beads to white beads is \(4:1:3\). So:
• Gold \(= 4y\)
• Green \(= y\)
• White \(= 3y\)
Total \(= 8y\)
Across the two containers combined, the number of gold beads equals the number of green beads. So:
\(x + 4y = 3x + y\)
\(3y = 2x\)
\(x = \frac{3y}{2}\)
So the total number of beads in Container 1 is:
\(6x = 6 * \frac{3y}{2} = 9y\)
The total number of beads in Container 2 is:
\(8y\)
Therefore, the totals in Container 1 and Container 2 must be in the ratio \(9:8\). Check the options for a \(9:8\) ratio pair.
• The pair 45 and 40 has the ratio \(9:8\), but 45 cannot be the total for Container 1 because Container 1’s total must be a multiple of 6.
• The pair 72 and 64 has the ratio \(9:8\), and 72 is a multiple of 6 while 64 is a multiple of 8.
• The pair 81 and 72 has the ratio \(9:8\), but 81 cannot be the total for Container 1 because Container 1’s total must be a multiple of 6.
Correct answer:
Container 1 "72"
Container 2 "64"
