How do you solve this Pre-Algebra problem:

$1.25x + $2.25y = $916
x + y = 560

This is a system of equations. There are three ways you can solve these types of problems, graphing, substitution, or elimination. I'll use eliminations for this one. Elimination means that you try to eliminate one of the variables.

First, I multiply the second equation by 1.25:

1.25x + 2.25y = 916
1.25x + 1.25y = 700

Now, subtract the two equations:

1y = 216

y = 216

Substitute 216 into y of one of the equations:

1.25x + 2.25(216) = 916

1.25x + 486 = 916

1.25x = 430

x = 344

The answer is (344, 216).

Check your answer by substituting these values into the equations:

1.25(344) + 2.25(216) = 916

Yes

344 + 216 = 560

Yes

the ratio of the length to the width of a rectangular field is 3 to 2, if the field is 120 yards long, how wide is the field.

To solve the system of equations:

Step 1: Solve the second equation for x:
x + y = 560
x = 560 - y

Step 2: Substitute the value of x from Step 1 into the first equation:
$1.25(560 - y) + $2.25y = $916

Simplify the equation:

$700 - $1.25y + $2.25y = $916

Combine like terms:

$700 + $1.00y = $916

Step 3: Solve for y by subtracting $700 from both sides:
$1.00y = $216

Step 4: Divide both sides by $1.00 to get the value of y:
y = $216 / $1.00
y = 216

Step 5: Substitute the value of y into the second equation to find x:
x + 216 = 560

Step 6: Solve for x by subtracting 216 from both sides:
x = 560 - 216
x = 344

Therefore, the solution to the system of equations is x = 344 and y = 216.

To solve this Pre-Algebra problem, we can use the method of substitution or elimination. Let's use the method of substitution.

Step 1: Solve one of the equations for one variable in terms of the other variable.
We have the equation x + y = 560. Let's solve for x:
x = 560 - y

Step 2: Substitute the expression for that variable in the other equation.
Substitute x = 560 - y into the equation $1.25x + $2.25y = $916:

$1.25(560 - y) + $2.25y = $916

Step 3: Simplify and solve for the remaining variable.
Distribute $1.25:
$700 - $1.25y + $2.25y = $916

Combine like terms:
$1.00y = $216

Step 4: Solve for y.
Divide both sides by $1.00 to isolate y:
y = $216 / $1.00

Simplify:
y = 216

Step 5: Substitute the value of y back into one of the original equations to solve for the other variable.
Using the equation x + y = 560:
x + 216 = 560

Subtract 216 from both sides:
x = 560 - 216

Simplify:
x = 344

So the solution to the system of equations is x = 344 and y = 216.