I can't figure out how to solve this problem.?

Question

I have to translate the word problem to a system of two equations and then solve it.

The price of a sweater is $5 less than twice the price of a shirt. If four shirts and three sweaters cost $275, find the price of each shirt and each sweater.

Answer 1

Sweater=y
Shirts=x
Here are the 2 systems of equations
y=2x-5
4x+3y=275 Now substitute the y for the 1st equation
4x+3(2x-5)=275 Now use the distributive method
4x+6x-15=275 Now combine like terms
10x-15=275 Now add 15 to both sides
10x=290 Now divide both sides by 10
x=29 Now substitute the x in the y=2x-5 for 29
y=2(29)-5 now multiply 2x29
y=58-5
y=53
Shirts are $29
Sweaters are $53

Note: I used the substitution meathod. Ecolink used the elimination meathod. Both are correct and will get you the right answer.

Answer 2

Make TWO EQUATIONS out of what the problem tells you.
It's not the shortest way, but it's what the problem says to do.

Let x be the price of a sweater.
Let y be the price of a shirt.

The price of a sweater is $5 less than twice the price of a shirt.
x = 2y - 5

If four shirts and three sweaters cost $275
4y + 3x = 275

Now solve the system
x = 2y - 5 Change order to match other equation.

-2y + x = -5 Multiply this equation by 2.

-4y + 2x = -10
4y + 3x = 275 Add the two equations.

5x = 265
x = 53

Substitute 53 for x in first equation.
x = 2y - 5
53 = 2y - 5
58 = 2y
29 = y

Check by seeing if the second equation is right with 53 and 29.

4y + 3x = 275
4*29 + 3*53 = 275
116 + 159 = 275

Answer 3

say X equals the price of the shirt.
then, X-5 is the price of the sweater, since its $5 less than the shirt.
that means, 4X + 3(X-5) = 275. with the distrubutive prop, 4X + 3X - 15 = 275, so 7X = 290