Write linear equations to solve word problems
Learn with an example
Monica has already baked 26 pies, and she can bake 4 pies with each additional cup of sugar she buys. With 12 additional cups of sugar,
how many total pies can Monica bake? Write and solve an equation to find the answer.
____ pies
Make a chart.
| Additional cups of sugar (s) | Calculation of number of pies (p) | Number of pies (p) |
| 0 | 4(0) + 26 | 26 |
| 1 | 4(1) + 26 | 30 |
| 2 | 4(2) + 26 | 34 |
| s | 4(s) + 26 | 4s + 26 |
Find the pattern: p is 4 times s, plus 26.
Write this relationship as an equation.
| p is 4 times s, plus 26 |
| ↓ |
| p = 4s + 26 |
Now plug s = 12 into this equation and solve for p.
p = 4s + 26
p = 4(12) + 26 Plugin s = 12
p = 48 + 26 Simplify
p = 74
With 12 additional cups of sugar, Monica can bake a total of 74 pies.
Zane takes 2 quizzes each week.
Write an equation that shows the relationship between the number of weeks w and the total number of quizzes q.
Make a chart.
| Number of weeks (w) | Calculation of total number of quizzes (q) | Total number of quizzes (q) |
| 1 | 2(1) | 2 |
| 2 | 2(2) | 4 |
| 3 | 2(3) | 6 |
| w | 2(w) | 2w |
Find the pattern: q is 2 times w.
Write this relationship as an equation.
| q is 2 times w |
| ↓ |
| q = 2w |
Noah has already taken 7 pages of notes on his own, and he will take 2 pages during each hour of class.
Write an equation that shows the relationship between the time in class h and the number of pages p.
Write your answer as an equation with p first, followed by an equals sign._____
Make a chart.
| Time in class (h) | Calculation of number of pages (p) | Number of pages (p) |
| 0 | 2(0) + 7 | 7 |
| 1 | 2(1) + 7 | 9 |
| 2 | 2(2) + 7 | 11 |
| h | 2(h) + 7 | 2h + 7 |
Find the pattern: p is 2 times h, plus 7.
Write this relationship as an equation.
| p is 2 times h, plus 7 |
| ↓ |
| p = 2h + 7 |
Let’s Practice!
