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Math  /  Algebra

QuestionPart C: The basketballs Noah packed had two different prices. Of the total number of basketballs sold, 60%60 \% had a price that was $21\$ 21 more than the price of the remaining basketballs. The total amount of the store's sales for all the basketballs was $8,967\$ 8,967. What was the price for one of the more expensive basketballs? Enter answer here:

Studdy Solution

STEP 1

1. Let x x be the price of the less expensive basketball.
2. The more expensive basketballs are priced at x+21 x + 21 .
3. 60% of the basketballs sold were the more expensive type.
4. The total sales amount for all basketballs was \$8,967.
5. We need to find the price of one of the more expensive basketballs.

STEP 2

1. Define variables for the prices and quantities of basketballs.
2. Set up an equation based on the total sales.
3. Solve the equation for the price of the more expensive basketball.

STEP 3

Define variables for the prices and quantities of basketballs.
Let x x be the price of the less expensive basketball. Then, the price of the more expensive basketball is x+21 x + 21 .

STEP 4

Set up an equation based on the total sales.
Assume the total number of basketballs sold is n n . Then, 60% of the basketballs, or 0.6n 0.6n , were sold at the price x+21 x + 21 , and the remaining 40%, or 0.4n 0.4n , were sold at the price x x .
The total sales equation is:
0.6n(x+21)+0.4nx=8967 0.6n(x + 21) + 0.4nx = 8967

STEP 5

Simplify and solve the equation.
Distribute the terms:
0.6nx+12.6n+0.4nx=8967 0.6nx + 12.6n + 0.4nx = 8967
Combine like terms:
nx+12.6n=8967 nx + 12.6n = 8967

STEP 6

Solve for x x .
Rearrange the equation to isolate nx nx :
nx=8967−12.6n nx = 8967 - 12.6n
Since n n is the total number of basketballs, divide both sides by n n to solve for x x :
x=8967−12.6nn x = \frac{8967 - 12.6n}{n}
Now substitute back to find the price of the more expensive basketball:
x+21=8967−12.6nn+21 x + 21 = \frac{8967 - 12.6n}{n} + 21

STEP 7

To find the specific price, we need additional information about n n . However, since the problem asks for the price of the more expensive basketball, we assume n n is such that the equation is solvable with the given total sales.
If n n is known or can be estimated, substitute it into the equation to find x x and then x+21 x + 21 .
Solution: The price of one of the more expensive basketballs is x+21 x + 21 . Without additional information about n n , the exact numerical answer cannot be determined from the given data alone.

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