she mixes 2 1/2 of grape with 1 1/2 of orange. grape cost $1 more than orange. total cost is $12.50

Question

im in 8th grade so yeah

Answer 1

let r = orange; g = grape.

Here's what we know:

g = r + 1

2.5g + 1.5r = 12.5

 

We have a value for g, so let's plug that in:

2.5(r +1) + 1.5r = 12.5

Distribute:

2.5r + 2.5 + 1.5r = 12.5

Simplify:

4r + 2.5 = 12.5

Subtract 2.5 from both sides:

4r = 10

Divide by 4:

r = 2.5

 

Now we can solve for g:

g = 2.5 + 1

g = 3.5

 

Now to check:

2.5 * 3.5 + 1.5 * 2.5 = 12.50

8.75 + 3.75 = 12.50

12.50 = 12.50

Answer 2

Hi,

This Math problem can be written and solved as a system of 2 linear equations with 2 unknown variables X (grape cost) and Y (orange cost)

 

(2 1/2)X + (1 1/2)Y = 12.5

X - Y = 1

 

You can solve this system of linear equations by using online equations solver, which accepts input as fractions, mixed numbers and decimals (http://examn8.com/SystemOfEquations.aspx). The result would be X = 3 1/2 (grape cost) and 2 1/2 (orange cost). 

 

Alternatively, you can convert everything to the decimals and solve it:

 

2.5X + 1.5Y = 12.5

X-1 = 1

 

resulting in the same: X = $3.50 and Y = $2.50

 

Hope this will help.