An algebra problem by Noah Smalls
Eric and Marie just had business cards made. Eric's printing company charged a one-time setup fee of $13 and then $7 per box of cards. Marie, meanwhile, ordered hers online. They cost $5 per box. There was no setup fee, but she had to pay $15 to have her order shipped to her house. By coincidence, Eric and Marie ended up spending the same amount on their business cards. How many boxes did each buy? How much did each spend?
Ex. (25,$50) - The 25 will represent the x-value or the number of boxes they bought and $50 represent y-value or how much did each spent.
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1 solution
To solve using substitution, follow these four steps:
Step 1: Isolate a variable.
Step 2: Plug the result of Step 1 into the other equation and solve for one variable.
Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.
Step 4: State the solution. Before you can solve, you must write a system of equations. Let x = boxes, and let y = dollars.
y = 7x + 13 y = 5x + 15
Now use substitution to solve the system of equations.
Step 1: Isolate a variable.
The variable y is already isolated in the first equation.
Step 2: Plug the result of Step 1 into the other equation and solve for one variable.
Plug = 7x + 13 into the other equation, y = 5x + 15 , and find the value of x . y = 5x + 15
7x + 13 = 5x + 15 Plug in = 7x + 13
2x + 13 = 15 Subtract 5x from both sides
2x = 2
Subtract 13 from both sides x = 1
Divide both sides by 2
Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable. Take the result of Step 2, x = 1, and plug it into one of the original equations, such as y = 7x + 13. Then find the value of y.
y = 7x + 13
y = 7(1) + 13 Plug in = 1
y = 7 + 13 Multiply
y = 20 Add
Step 4: State the solution.
Since x = 1 and y = 20, the solution is (1, 20).
Eric and Marie each bought 1 box of business cards, spending $20.