made $800 selling t shirts and caps. They sold 200 shirts and 60 caps. how many youth shirts did they sell?

Question

Adults Shirts $4 youth $3 caps $2. How many youth shirts were sold?

Answer 1

a = adult shirts
y = youth shirts
c = caps

1st equation: $4 per adult shirt, so they made $4*a from adult shirts... $3*y for youth shirts, and $2*c for caps...
4a + 3y + 2c = 800

we know they sold 60 caps...
c = 60

and we know they sold a total of 200 shirts...
a + y = 200

since caps are $2 and they sold 60...
4a + 3y + 2(60) = 800
4a + 3y + 120 = 800
4a + 3y = 680

Now we have 2 variables and 2 equations:
a + y = 200
4a + 3y = 680

a = 200 - y
4 (200 - y) + 3y = 680
800 - 4y + 3y = 680
-y = -120
y = 120

so they sold 120 youth and 80 adult

Check:

120 * 3 + 80 * 4 + 60 * 2 = 360 + 320 + 120 = 800

Hope this helps!

Answer 2

Let x = Adult Shirts.
Let y = Youth Shirts.

x + y = 200 (1)
4x + 3y + 120 = 800
4x + 3y = 680 (2)

Substitute (1) now inside of 2. I will isolate x as x = 200 - y from equation 1.
4(200 - y) + 3y = 680
800 - 4y + 3y = 680
800 - y = 680
120 = y (120 youth shirts were sold).
x + 120 = 200
x = 80
80 adult shirts were sold.

Proof:
80 * 4 = 320
120 * 3 = 360
Total = 680.

Add in the 60 hats sold at $2 each, you get 680 + 120 = $800.
BAM!!! Enjoy the explanation.

Answer 3

200x + 60y = 800

Answer 4

do ur own homework