Question

Ray bought two kinds of tennis balls at 2 different prices. The Bouncies cost $3 for a set, and the Yellows cost $5 for each set. How many sets of balls did Ray purchase if he spent a total of $49 on 11 sets of tennis balls?

a) Number of Bouncies: 8

b) Number of Yellows: 3

c) Number of Bouncies: 5

d) Number of Yellows: 6

Answer 1

Ray bought 3 sets of Bouncies and 8 sets of Yellows.

Step-by-step explanation:

Let's assume Ray bought x sets of Bouncies and y sets of Yellows.

The cost of x sets of Bouncies is 3x ($3 for each set).

The cost of y sets of Yellows is 5y ($5 for each set).

Since Ray spent a total of $49 on 11 sets of tennis balls, we can write the equation: 3x + 5y = 49.

We also know that Ray bought a total of 11 sets of tennis balls: x + y = 11.

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method.

1. Multiply the second equation by 3: 3(x + y) = 3(11) = 33.
2. Subtract the second equation from the first equation: (3x + 5y) - (3x + 3y) = 49 - 33.
3. Simplify: 2y = 16.
4. Divide both sides by 2: y = 8.
5. Substitute the value of y into the second equation: x + 8 = 11.
6. Subtract 8 from both sides: x = 3.

Therefore, Ray bought 3 sets of Bouncies and 8 sets of Yellows.