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Chapter 5: Problem 130

A mix for eight servings of instant potatoes requires \(2 \frac{2}{3}\) cups of water. Use this information to solve. If you want to make six servings, how much water is needed?

Short Answer

Expert verified
You need 2 cups of water to make six servings of instant potatoes.

Step by step solution

01

Understand the Proportion

Recognize that the problem presents a ratio: eight servings of instant potatoes requires \(2 \frac{2}{3} \) cups of water. This ratio can be written as \( \frac{8}{2 \frac{2}{3}} \).
02

Convert Mixed Fraction to Improper Fraction

Convert \(2 \frac{2}{3} \) cups of water to an improper fraction to make calculations easier. \( 2 \frac{2}{3} \) converts to \( \frac{8}{3} \) cups.
03

Setup a Proportional Equation

Since we know the ratio of servings to water, we can scale this ratio down to find the amount of water corresponding to six servings. This leads to the equation \( \frac{8}{\frac{8}{3}} = \frac{6}{x} \).
04

Solve the Proportional Equation

Cross-multiply and solve the equation for x. This gives \( x = \frac{6}{8}*\frac{8}{3} = 2 \).

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Most popular questions from this chapter

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=2, r=0.1\)

If you are given a sequence that is arithmetic or geometric, how can you determine which type of sequence it is?

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=1000, r=-\frac{1}{2}\).

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{30}\), when \(a_{1}=8000, r=-\frac{1}{2}\).

Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(1,5,9,13, \ldots\)
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