A person sees the price of a pair of pants and a shirt at $2,200 for both. If a month later there are sales in the store with 20% on the pants and 10% on the shirt and I pay $1800, how much money was saved on the shirt?
Accepted Solution
A:
ANSWER
$40
Step by Step
Let's break down the problem step by step:
Initially, the person sees the price of a pair of pants and a shirt at $2,200 for both. Let's denote the price of the pants as "P" and the price of the shirt as "S."
So, we have:
P + S = $2,200
A month later, there are sales in the store with a 20% discount on the pants and a 10% discount on the shirt. After these discounts, the person pays $1,800 for both items.
1. For the pants, there is a 20% discount, which means the person pays 80% of the original price for the pants. So, the price of the pants after the discount is:
0.80 * P
2. For the shirt, there is a 10% discount, which means the person pays 90% of the original price for the shirt. So, the price of the shirt after the discount is:
0.90 * S
The total cost after the discounts is $1,800, so we have:
0.80 * P + 0.90 * S = $1,800
Now, we can set up a system of two equations with two variables:
1. P + S = $2,200
2. 0.80 * P + 0.90 * S = $1,800
We can solve this system of equations to find the values of P and S.
First, let's solve Equation (1) for P:
P = $2,200 - S
Now, substitute this expression for P into Equation (2):
0.80 * ($2,200 - S) + 0.90 * S = $1,800
Now, solve for S:
0.80 * $2,200 - 0.80 * S + 0.90 * S = $1,800
0.80 * $2,200 + 0.10 * S = $1,800
Now, subtract 0.80 * $2,200 from both sides:
0.10 * S = $1,800 - 0.80 * $2,200
0.10 * S = $1,800 - $1,760
0.10 * S = $40
Now, divide both sides by 0.10 to find the price of the shirt (S):
S = $40 / 0.10
S = $400
So, the original price of the shirt was $400.
Now, to find how much money was saved on the shirt, we need to calculate the discount amount:
Original price of the shirt - Price of the shirt after discount = Savings on the shirt
$400 - 0.90 * $400 = $400 - $360 = $40
The person saved $40 on the shirt.