Before you can solve, you must write simultaneous equations. Let x represent hours, and let y represent pages.
y = 5x + 51
y = 15x + 41
Now use substitution to solve the simultaneous 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 y = 5x + 51 into the other equation, y = 15x + 41, and find the value of x.
y = 15x + 41
5x + 51 = 15x + 41
Plug in y = 5x + 51
–10x + 51
= 41 Subtract 15x from both sides
–10x = –10 Subtract 51 from both sides
x = 1 Divide both sides by –10
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 = 5x + 51. Then find the value of y.
y = 5x + 51
y = 5(1) + 51 Plug in x = 1
y = 5 + 51 Multiply
y = 56 Add
Step 4: State the solution.
Since x = 1 and y = 56, the solution is (1, 56).
After 1 hour, Cole and Terrence will have each completed 56 pages in their workbooks.
