SOLUTION: Mike bought some kilograms of apples and some kilograms of oranges and spent $27.25. The apples cost $3.10 per kilogram and oranges cost $4.95 per kilogram. If apples become $1

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Mike bought some kilograms of apples and some kilograms of oranges and spent $27.25. The apples cost $3.10 per kilogram and oranges cost $4.95 per kilogram. If apples become $1      Log On


   

Question 211973: Mike bought some kilograms of apples and some kilograms of oranges and spent
$27.25. The apples cost $3.10 per kilogram and oranges cost $4.95 per kilogram.
If apples become $1.55 more expensive and oranges become $1.15 chaper he will
spend $30. How many ograms of apples and oranges did Mike buy?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Mike bought some kilograms of apples and some kilograms of oranges and spent
$27.25. The apples cost $3.10 per kilogram and oranges cost $4.95 per kilogram.
If apples become $1.55 more expensive and oranges become $1.15 cheaper he will
spend $30. How many kilograms of apples and oranges did Mike buy?

1. Let x=number of kilograms of apples and y=number of kilograms of oranges.

2. Cost of apples = x*$3.10 =3.10x

3. Cost of oranges= y*4.95=4.95y

4. Total cost = 27.25 = 3.10x+4.95y

5. Let's look at "If apples become $1.55 more expensive and oranges become $1.15 cheaper he will spend $30."

a. For apples 3.10+1.55=4.65

b. For oranges 4.95-1.15=3.80

c. New total cost = 30 = 4.65x+3.80y

d. Note we still have the same number of apples x and oranges y.

6. So now we have two equations and two unknowns

a. 27.25 = 3.10x+4.95y

b. 30 = 4.65x+3.80y

Need to solve for x and y. The steps below will show x=4 and y=3


Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 4.95*y to the right, we get:
3.1%2Ax+=+27.25+-+4.95%2Ay, or x+=+27.25%2F3.1+-+4.95%2Ay%2F3.1. Substitute that
into another equation:
4.65%2A%2827.25%2F3.1+-+4.95%2Ay%2F3.1%29+%2B+3.8%5Cy+=+30 and simplify: So, we know that y=3. Since x+=+27.25%2F3.1+-+4.95%2Ay%2F3.1, x=4.

Answer: system%28+x=4%2C+y=3+%29.




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