SOLUTION: 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 $22.5 pe

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Question 1021109: 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 $22.5 per helmet. the sales tax 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 by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

the cost per baseball is 2.25.
the cost per baseball hat is 22.5.

since you need to keep the ratio between baseballs and hats to 8/3, then find the price of 8 baseballs and 3 baseball hats.

the price of 8 baseballs is 8 * 2.25 = 18 dollars.

the price of 3 baseball hats is 3 * 22.5 67.5.

the total cost of one set of 3 baseball hats and 8 baseballs is 18 + 67.5 = 85.5 dollars.

400 / 85.5 = 4.67..... which you want to round down to 4.

the largest number of complete sets of 8 baseballs and 3 baseball hats is 4.

you will pay 4 * 85.5 = 342 dollars.

you will have 400 - 342 = 58 dollars left.

you could have solved this algebraically as follows:

b = number of baseballs.
h = number of baseball hats.
s = one set of 8 baseballs and 3 baseball hats.

cost of one baseball is 2.25.
cost of 1 baseball hat is 22.5.

cost of one set of 8 baseballs and 3 baseball hats is 8 * 2.25 + 3 * 22.5 = 85.5.

your equation is 85.5 * s = 400

divide both sides of this equation by 85.5 to get s = 4 plus a remainder.

the most number of sets you can get is 4.

4 * 8 = 32 baseballs.
4 * 3 = 12 baseball hats.

32 * 2.25 = 72
12 * 22.5 = 270

total is 342.

same as above.

placing the baseballs and baseball hats into sets of 8 baseballs and 3 baseball hats each is the simplest way to solve this problem as far as i can see.

then it's simply a matter of determining the maximum number of complete sets you can buy with your 400.

i forgot the tax.

tax is 6%.

342 * .06 = 20.52.

total cost is 342 + 20.52 = 362.52.

still remains at 4 complete sets as the maximum you can buy at the reduced price.