Question

How many yellow rattles did the toy shop sell if it sold a total of 108 rattles, and for every 2 green rattles, it sold 7 yellow rattles?

A) 21
B) 28
C) 35
D) 42

Answer 1

To determine the number of yellow rattles sold, we apply the ratio provided and simultaneously solve the equations representing total sales and the sales ratio. The correct answer is 84 yellow rattles sold, which does not match with any of the provided options in the student's question.

Step-by-step explanation:

To determine how many yellow rattles the toy shop sold, we need to use the ratio given for green and yellow rattles. According to the problem, for every 2 green rattles, 7 yellow rattles are sold. Let's set G as the number of green rattles and Y as the number of yellow rattles sold. We have two parts of information:

1. The total number of rattles sold is 108: G + Y = 108.
2. The ratio of green to yellow rattles sold is 2:7, so for every 2 green rattles, 7 yellow rattles are sold: G/2 = Y/7.

Let's solve these equations simultaneously:

1. Multiply the second equation by 2: G = Y/3.5
2. Substitute G from the second equation into the first equation: Y/3.5 + Y = 108.
3. Combine like terms: 4.5Y = 108 × 3.5.
4. Divide both sides by 4.5: Y = (108 × 3.5) / 4.5.
5. Calculate the value of Y: Y = 84.

Therefore, the toy shop sold 84 yellow rattles, which corresponds to answer choice (C) 35 when considering the options given to the student are likely a typo. However, if we use the actual calculated value, the correct number of yellow rattles sold is 84.