Shreya C.

Period 7

Algebra 1-2

Solving Word Problems Using Systems of Equations

Suppose you are starting a daycare center. You have spent $1500 on equipment and materials for the children. You spend $10/day on food. Your total income is $50/day. How many days will it take you to break even?

First, define your variable

Let d= number of days

Then, write your equations

Your income per day is $50

Income= 50d

You have spent $1500 on equipment and you spend $10 each day on food

Expense= 1500+10d

Expense=Income; to find the break even point expenses must be the same as your income

1500+10d=50d

Next, Solve the equation

1500+10d=50d

-10d -10d ß Combine the variables

ß Divide to isolate variable

37.5 = d ß Solution

Answer: It will take 37.5 days to break even

After that, Find the amount where you will break even

Substitute the number of days into one of the equations

Income= 50d

= 50(37.5)

= 1875 dollars

In 37.5 days and $1875 you will break even

Then, figure out how to earn a profit

Substitute a high number than the answer into an equation

Expense= 1500+10d

= 1500+10(38)

= 1500+380

= 1880 dollars ßHigher than break even point; made a profit

If you run the daycare center for more than 37.5 days, you will make a profit

Another way to solve this problem is by creating a graph