Question

While Shopping Margaret bought a total of 10 items ( pants and t shirts) each pair of pants cost $53, each shirt is $27. She spent $374. How many pants and How many shirts.

Answer 1

Given that she bought a total of 10 items ( pants and t-shirts) each pair of pants cost $53, each shirt is $27. She spent $374, we have two linear equations as follows:

Let x be the number of pants and let y be the number of t-shirts, then:

$53x+27y=374$$x+y=10$

In order to find how many and shirts she bought, we have to solve this linear system of two equations and two variables:

$53x+27y=374\rightarrow53x=374-27y\rightarrow x=\frac{374-27y}{53}$$\mathrm{Substitut}e\mathrm{\:}x=\frac{374-27y}{53}\text{ }into\text{ x + y = 10}$$\frac{374-27y}{53}+y=10$$\frac{374+26y}{53}=10$$\mathrm{Isolate}\:y$$\frac{53\left(374+26y\right)}{53}=10\cdot \:53$$374+26y=530$$374+26y-374=530-374\rightarrow26y=156\rightarrow y=6$

then:

$x=10-y=10-6=4$

So, she bought 4 pants and 6 t-shirts.