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.