Three apples and two peaches cost $3.00. Four apples and one peach cost $2.75. Find the cost of each

Question

I know it is a system of equations problem. I need help with those equations

Answer 1

Let A=the price of an apple, P=the price of a peach.

 

Set up equations:

 

1) 3A + 2P=3.00

 

2) 4A + P=2.75

 

Multiply equation 2 by a factor of 2 to get equation 2A:

 

2A) 8A + 2P=5.50

 

Subtract equation 1 from equation 2A

 

8A + 2P=5.50

-3A  -2P=-3.00

 

5A=2.50

 

A=2.50/5 or 0.50; one apple costs 50 cents.

 

Use equations 1, 2, or 2A to solve for P.

 

3(0.50) + 2P=3.00

 

1.50 + 2P=3.00

-1.50       =-1.50

 

2P=1.50

 

P=1.50/2 or 0.75, one peach costs 75 cents.

Answer 2

You need to establish the 2 equations first:

 

Let x = the price of the apples and let y = the price of the peaches

 

3x + 2y = $3.00

4x + y = $2.75

 

Solve for one of the unknowns (I'd pick the bottom) and then substitute it in the other equation.

 

 4x + y = 2.75

 

y = 2.75 - 4x ---Substitute this one into the first one

 

 

3x + 2(2.75 - 4x) = 3.00 ---> Multiply 2 through out each term in parenthesis

 

3x + 5.50 - 8x = 3.00 ---> Subtract 3x - 8x to get -5x

 

5.50 - 5x = 3.00 ---> Subtract 5.50 from both sides

 

-5x = -2.50 ---> Divide both sides by -5

 

x = 0.50 ---> This is the price of the apple. 

 

After finding the price of the apple, use this to solve for y; or the price of the peach. 

 

y = 2.75 - 4x ---> x = 0.50

 

y = 2.75 - 4(0.50)

 

y = 2.75 - 2

 

y = 0.75 ---> Price of the peach

 

 

HOpe this helps!