Question

One fifth of a number plus three times the number is equal to twice the number plus 42. What is the number? Practice Think: What equation can you write to solve the problem?

Answer 1

For this problem, we will assign the number a letter to represent it: X

One fifth of x + 3 x’s equals 42 + 2 x’s
Translate that to:
1/5x +3x = 42+ 2x

Next, use algebra to solve this equation.
Start by multiplying everything by 5 to make all the x values whole numbers:
5x +15x = 210 + 10x

Next, add common factors of x:

20x = 210 + 10x

Then subtract 10 x’s from each side to make only one factor with x:

10x=210

Finally, divide by ten to make only one x:
X=21
The number is 21