In this section, you will learn how two-step equations can be solved.
We can use inverse operations to solve equations with more than one operation.
Example 1 :
Five less than the quotient of a number and 4 is 15. What is the number ?
Solution :
Step 1 :
Let n represent the number. Write an equation.
n/4 - 5 = 15
Step 2 :
n/4 - 5 = 15
Add 5 to both sides
(n/4 - 5) + 5 = 15 + 5
n/4 = 20
Multiply both sides by 4
4.(n/4) = 4.(20)
n = 80
Hence, the number is 80.
Example 2 :
The Wilsons have triplets and another child who is ten years old. The sum of the ages of their children is 37. How old are the triplets ?
Solution :
Step 1 :
Let m represent the age of each child in triplet. Write an equation.
3m + 10 = 37
Step 2 :
3m + 10 = 37
Subtract 10 on both sides
(3m + 10) - 10 = 37 - 10
3m = 27
Divide both sides by 3
3m/3 = 27/3
m = 9
So, the age of each child in the triplet is 9 years.
Example 3 :
A dog sled driver added more gear to the sled, doubling its weight. This felt too heavy, so the driver removed 20 pounds to reach the final weight of 180 pounds. Write and solve an equation to find the sled’s original weight.
Solution :
Step 1 :
Let w represent the original weight of the sled. Write an equation.
2w - 20 = 180
Step 2 :
2w - 20 = 180
Add 20 to both sides
(2w - 20) + 20 = 180 + 20
2w = 200
Divide both sides by 2
2w/2 = 200/2
w = 100
So, the sled’s original weight was 100 pounds.
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