Question

A softball team bought 24 jerseys and 15 hats for a total cost of $1713. Later, they bought 5 more jerseys and 12 more hats for a total cost of $490. If the cost per item was the same for each order, what was the cost of each jersey and each hat ?

Answer 1

x represents jerseys, y represents hats

x= $62 y=$15

Explanation:

Now I used a matrix (linear algebra), but I think elimination is better for you

So the idea of elimantion is so that both side have one variable that is the same

so we know that the equations are

4(24 x + 15y = 1713)

-5(5x + 12x = 490)

Multiply first equation by 4 and second equation by -5

If two of the varblies have opposite signs it means you are adding, but its subtracting if they have the same signs!

96x+60y=6852

+ −25x−60y=−2450

71x + 0y =4402

71x/71 = 4402/71

x= 4402/71

x=62

Now that we know this, we can plug into any other the orignial equation of x to get y.

I'll use the first one

24x+15y=1713

substitute 62 for x

(24)(62)+15y=1713

15y+1488=1713(Simplify both sides of the equation)

bring 1488 to the other side (swaps signs)

15y= 1713−1488

15y=225

15y/15 = 225/15

y= 15

Therefore, x= 62 and y= 15 or cost of the jerseys is $62 each and cost of hats is $15 each.