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%. Couch 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?

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opudodennis opudodennis · Answer 1 · 2020-03-19T13:44:08+01:00

Answer:

Helmets-12

Baseballs-32

Step-by-step explanation:

Given the tax rate as 6% and the reduced prices as $2.25/baseball and $22.50/helmet and that the budget is $400:

The new prices are reduced price plus tax:

[tex]Baseball \ Price =2.25\times (1.06\%)=2.39\\\\Helmet \ Price= 22.50\times (1.06\%)=23.85[/tex]

Let x be the number of groups of 8 baseballs as well as the number of groups of 3 helmets,therefore:

[tex]8x(2.39)+3x(23.85)=400\\\\19.12x+71.55x=400\\\\x=4.4116\\\\x\approx 4[/tex]

Substitute for x=4 to find the highest number of baseballs and helmets:

Helmets=4x3=12

Baseball=4x8=32

#Price cost will be 12x23.85+32x2.39=362.68 (balance=37.32)

Hence, Shaw can buy 12 helmets and 32 baseballs and still remain with $37.32