Problem 83
Question
Use the given information to write an equation. Let \(x\) represent the number described in each exercise. Then solve the equation and find the number. When one-third of a number is added to one-fifth of the number, the sum is \(16 .\) What is the number?
Step-by-Step Solution
Verified Answer
The number is 30.
1Step 1: Set up the Equation
Write the equation based on the given problem: \(\frac{1}{3}x + \frac{1}{5}x = 16\).
2Step 2: Simplify the Equation
Convert the fractions to have a common denominator, which is 15 in this case. The equation becomes \(\frac{5}{15}x + \frac{3}{15}x = 16\), which further simplifies to \(\frac{8}{15}x = 16\).
3Step 3: Solve for x
Solve for x by multiplying both sides of the equation by the reciprocal of \(\frac{8}{15}\), which is \(\frac{15}{8}\). This gives: \(x = 16 * \frac{15}{8} = 30\).
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