Question 1021109

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.