The price of a sweater is $5 less than teice the price of a shirt. if four sweaters and three shirts cost $200, find the price of each shirt and each sweater.
sw+5=2sh
4sw+3sh=200
4(2sh-5)+3sh=200
solve for the shirt price, then go back and solve for sw.
$20, $35 The shirts are $20 and the sweaters are $35
To solve this problem, we can set up a system of equations using the given information.
Let's represent the price of a shirt as "x" and the price of a sweater as "y".
The first equation we can write is: "The price of a sweater is $5 less than twice the price of a shirt."
This can be represented as: y = 2x - 5.
The second equation comes from the statement: "Four sweaters and three shirts cost $200."
Since four sweaters cost 4y and three shirts cost 3x, we can write the equation as: 4y + 3x = 200.
Now we have a system of two equations:
y = 2x - 5 ...(Equation 1)
4y + 3x = 200 ...(Equation 2)
To solve this system of equations, we can use substitution or elimination method. Let's use substitution method:
Step 1: Substitute the value of y from Equation 1 into Equation 2.
4(2x - 5) + 3x = 200
Step 2: Simplify the equation.
8x - 20 + 3x = 200
11x - 20 = 200
Step 3: Move the constant term to the other side.
11x = 200 + 20
11x = 220
Step 4: Solve for x by dividing both sides by 11.
x = 220 / 11
x = 20
Now we know the price of a shirt is $20.
Step 5: Substitute the value of x back into Equation 1 to find y.
y = 2(20) - 5
y = 40 - 5
y = 35
Therefore, the price of a sweater is $35.
In conclusion, the price of each shirt is $20 and the price of each sweater is $35.