Question

Mr. Gretzky spent $390 on 5 similar basketballs and 4 similar volleyballs. Each basketball costs $15 more than each volleyball. What is the price of a basketball and the price of a volleyball

Answer 1

Given:

Mr. Gretzky spent $390 on 5 similar basketballs and 4 similar volleyballs

Cost of each basketball is $15 more than the cost of each volleyball

To find:

The price of a basketball and the price of a volleyball

Solution:

Let's assume,

"b" → represent the price of each basketball

"v" → represent the price of each volleyball

Since for 5 basketballs and 4 volleyballs, Mr. Gretzky had spent $390, so we can write the eq. as,

5b + 4v = 390 ....... (i)

Also given that, the price of 1 basketball is $15 more than the price of 1 volleyball, so another equation that can be formed is,

b = v + 15

⇒ b - v = 15 ...... (ii)

On multiplying 5 throughout the eq. (ii), we get

5b - 5v = 75 ....... (iii)

Now, subtracting eq. (iii) from (i), we get

5b + 4v = 390

5b - 5v =    75

-     +         -

-----------------------------

    9v = 315

-----------------------------

∴ v = $\frac{315}{9}$ = $ 35

Substituting the value of v in eq. (ii), we get

b - v = 15

⇒ b - 35 = 15

⇒ b = 35 + 15

⇒ b = $ 50

Thus,

$\boxed{\bold{The\:price\:of \:a\:basketball\:is\:\ \:50.}}$

$\boxed{\bold{The\:price\:of \:a\:volleyball\:is\:\ \:35.}}$

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