Question

aul bought 9 total shirts for a total of $72. Tee shirts cost $10 and long sleeve shirts cost $7. How many of each type of shirt did he buy? A. 5 tee shirts and 4 long sleeve shirts B. 3 tee shirts and 6 long sleeve shirts C. 7 tee shirts and 2 long sleeve shirts D. 4 tee shirts and 5 long sleeve shirts

Answer 1

Set up a system of equations:

$\text{Total shirts bought}$

$x + y = 9$

$\text{Total cost}$

$10x + 7y = 72$

x represents how many tee shirts were bought, and y represents how many long sleeve shirts were bought.

For the first equation, subtract y from both sides to get x by itself:

$x = 9 - y$

We'll now use substitution. Since x is equal to a value, we can substitute this value for the other equation:

$10(9-y) + 7y = 72$

Distribute the 10 to both terms in parentheses:

$10 \times 9 = 90$

$10 \times -y = -10y$

$90 - 10y +7y = 72$

Combine like terms:

$-10y + 7y = -3y$

$90 - 3y = 72$

Subtract 90 from both sides:

$-3y = -18$

Divide both sides by -3 to get y by itself:

$y = 6$

6 long sleeve shirts were bought.

Now you have a value for y. Input this value into the first equation:

$x + 6 = 9$

Subtract both sides by 6 to get x by itself:

$x = 3$

3 tee shirts were bought.

The answer is B. 3 tee shirts and 6 long sleeve shirts.

Answer 2

Let’s look at the combinations of shirts and see if they add up to 72.
A. 5*10=50,4*7= 24, 50+24=74 So, it can’t be A.
B. 3*10=30,6*7=42, 30+42=72. So, it can be B... but let’s check the others too!
C. 7*10=70, 2*7=14, 70+14=84. So, not C.
D. 4*10=40, 5*7=35, 40+35=75.
So, the answer is B. 3 T-shirts and 6 long sleeve shirts! Hope this helped!