Question

8 shirts and 5 pairs of pants cost $695 altogether. 3 shirts and 3 pairs of pants cost $300 altogether. How much more does each shirt cost than each pair of pants

Answer 1

For this, we will be doing a system of equations. First will represent the total cost of $695 and the other will represent the total cost of $300.

Let s = cost of shirts and p = cost of pants:

$8s+5p=695\\ 3s+3p=300$

For this, I'll be using the substitution method. So firstly, subtract 3p on both sides of the second equation: $3s=300-3p$

Next, divide both sides of the second equation by 3: $s=100-p$

Now replace s in the first equation with (100-p). From here we can solve for p: $8(100-p)+5p=695$

Firstly, foil 8(100-p): $800-8p+5p=695$

Next, combine like terms: $800-3p=695$

Next, subtract 800 on both sides of the equation: $-3p=-105$

Next, divide both sides by -3, and your answer should be: $p=35$

Now that we know what the cost of pants is, we can replace p in either equation with 35 to solve for s. For this, I'll be using the second equation.

$3s+3(35)=300\\ 3s+105=300\\ 3s=195\\ s=65$

To find the difference in price, just subtract the prices: 65 - 35 = 30.

In short, shirts are $30 more expensive than pants.