write 2 equations based on the information I give you. Then solve this system.?

Question

How many shirts and hats must I make to satisfy both conditions?

I want to sell Timberwolf t-shirts for $25 each and Timberwolf hats for $10 each. I want to make $15,000 from the sale of the shirts and hats. I have a total of 750 hats and shirts (that is, the number of shirts + number of hats equals 750). Let's let x be the number of t-shirts and y be the number of hats.

Answer 1

15000 = 25x + 10y (total value)
750 = x + y (quantity)

15000 = 25x + 10y
7500 = 10x + 10y

7500 = 15x
500 = x

7500 = 10(500) + 10y
7500 = 5000 + 10y
2500 = 10y
250 = y

Sell 500 t-shirts and 250 hats

Answer 2

let us say that shirts = x and hats = y.

so...we know that x + y = 750...there is your first equation.

we can also write a cost equation. If each shirt is $25, then the cost of x shirts is 25x. keeping this in mind, your cost equations would be:
25x + 10y = 15000

so...your system of equations is:
x + y = 750
25x + 10y = 15000

now chose a method to solve...i will choose the elimination (aka addition or lin combination) method...

if you multiply the first equation through by -10, when you add the 2 equations together, the y will be eliminated and you can solve for x.

-10x + -10y = -7500
25x + 10y = 15000 --> add these 2 equations together

15x = 7500 -->divide by 15 to solve for x
x = 500

now if there are 500 shirts, to get 750, there would be 250 hats.

let us check this answer:
25(500) + 10(250) = 12500 + 2500 = 15000 this works

so the answer is
500 t-shirts and 250 hats

Answer 3

Tom was quicker. His solution is absolutely correct, but your question isn't, to be pedantic. You write "I want to make $15'000..." which I understand that you want to make a gain of that sum. Actually the turnover is $15'000, but you have from that money to pay the T-shirts and hats and perhaps also the rent of a shop.