The price of a sweater is $5 less than twice the price of a shirt. If four sweaters and three shirts cost $200, find the price of each skirt and each sweater.
I have no idea how to set up these types of equations..... someone please help its due tomorrow and i cant turn it in late
It will kill my grade... please help!!!
call r the cost of a sweater
call t the cost of a shirt
from the first fact:
r = 2 t - 5
from the second fact if I understand it:
4 r + 3 t = 200
substitute the first in the second
4 ( 2 t - 5 ) + 3 t = 200
8 t - 20 + 3 t = 200
11 t = 220
t = 20
then r = 2 t - 5 - 40-5 = 35
No need to worry, I'll explain the steps to solve this problem and set up the equations for you!
Let's start by assigning variables to the unknowns in the problem. Let's use:
- x for the price of a shirt
- y for the price of a sweater
Based on the given information, we can set up two equations:
1. "The price of a sweater is $5 less than twice the price of a shirt":
y = 2x - 5
2. "Four sweaters and three shirts cost $200":
4y + 3x = 200
Now we have a system of two equations with two unknowns. To solve it, we can use the method of substitution or elimination. Let's use substitution in this case.
Step 1: Substitute the value of y from equation 1 into equation 2:
4(2x - 5) + 3x = 200
Step 2: Simplify and solve for x:
8x - 20 + 3x = 200
11x - 20 = 200
11x = 220
x = 20
Step 3: Substitute the value of x into equation 1 to find y:
y = 2(20) - 5
y = 40 - 5
y = 35
Therefore, the price of each shirt is $20, and the price of each sweater is $35.