Question

Coach Shaw is buying baseball equipment for his team. he gets a reduced rate if he buys 8 baseballs for every 3 batting helmets. The reduced rate is $2.25 per baseball and $22.50 per helmet. The sales tax on each item is 6%. Coach Shaw has $400 in his budget to buy baseballs and helmets. What is the greatest number of baseballs and helmets he can buy at the reduced rate if the ratio of baseballs to helmets is 8:3?

Answer 1

$2.25x8=$18
$22.50x3=$67.50
Tax: 18x$0.06=$1.08~~~~$18+$1.08=$19.08.
67.50x0.06=4.05~~~~$67.50+$4.05=$71.55
$71.55+$19.08=$90.63
$400.00/$90.63= about 4 sets of 3 helmets and 8 baseballs.

Answer 2

He can by for sets, that is, 24 baseballs and 12 batting helmets.

Explanation:

We know that

Each baseball costs $2.25.

Each helmet costs $22.50.

This mean that 8 baseballs costs:
`8(\$2.25)=\$18\\`

And all 3 batting helmets costs:
`3(\$22.50)=\$67.50`

Now, one set of 8 baseballs and 5 helmets costs
`\$18 + \$67.50=\$ 85.50`

If coach Shaw has $400, the total number of set he can buy is
`(\$400)/(\$85.50)\approx 4`

This means he can by for sets, that is, 24 baseballs and 12 batting helmets.