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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

Respuesta :

kanest

Set up a system of equations:


[tex] \text{Total shirts bought} [/tex]

[tex] x + y = 9 [/tex]


[tex] \text{Total cost} [/tex]

[tex] 10x + 7y = 72 [/tex]


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:


[tex] x = 9 - y [/tex]


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


[tex] 10(9-y) + 7y = 72 [/tex]


Distribute the 10 to both terms in parentheses:


[tex] 10 \times 9 = 90 [/tex]

[tex] 10 \times -y = -10y [/tex]


[tex] 90 - 10y +7y = 72 [/tex]


Combine like terms:


[tex] -10y + 7y = -3y [/tex]

[tex] 90 - 3y = 72 [/tex]


Subtract 90 from both sides:


[tex] -3y = -18 [/tex]


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


[tex] y = 6 [/tex]


6 long sleeve shirts were bought.


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


[tex] x + 6 = 9 [/tex]


Subtract both sides by 6 to get x by itself:


[tex] x = 3 [/tex]


3 tee shirts were bought.


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

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