A bag contains three types of counter: purple squares, purple triangles and red triangles.
$70 %$ of the purple counters are triangles.
$60 %$ of the triangular counters are purple.
There are 14 red counters.
How many square counters are there?

Answer

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Answer

$9$ square counters in the bag.

Steps

Step 1 ：Let P be the number of purple counters, T be the number of triangular counters, and S be the number of square counters. We have the following equations:

Step 2 ： $0.7 P = 0.6 T$

Step 3 ： $0.4 T = 14$

Step 4 ：Solve the second equation for T: $T = \frac{14}{0.4} = 35$

Step 5 ：Substitute T into the first equation: $0.7 P = 0.6 (35)$

Step 6 ：Solve for P: $P = \frac{0.6 (35)}{0.7} = 30$

Step 7 ：Since there are 14 red triangles, there are $35 - 14 = 21$ purple triangles.

Step 8 ：Since 70% of the purple counters are triangles, there are $30 - 21 = 9$ purple squares.

Step 9 ： $9$ square counters in the bag.

A bag contains three types of counter: purple squares, purple triangles and red triangles.70% of the purple counters are triangles.60% of the triangular counters are purple.There are 14 red counters.How many square counters are there?

Answer

Popular Problems

A bag contains three types of counter: purple squares, purple triangles and red triangles.
$70 %$ of the purple counters are triangles.
$60 %$ of the triangular counters are purple.
There are 14 red counters.
How many square counters are there?