Five crates hold 20 pounds of materials. Jen set up this problem to find how many pounds of materials one crate holds:
[tex]$\frac{5}{20} = \frac{1}{x}$[/tex]
Which of the following best describes how Jen will continue to solve the problem?
A. Cross multiply, [tex]$5x = 20$[/tex]
B. Add across, [tex]$6 = 20x$[/tex]
C. Cross add, [tex]$5 + x = 21$[/tex]
D. Multiply across, [tex]$5 = 20x$[/tex]
Answer (1)
Set up the proportion: 20 5 = x 1 .
Cross multiply: 5 ⋅ x = 20 ⋅ 1 .
Simplify: 5 x = 20 .
The correct next step is: 5 x = 20 .
Explanation
Understanding the Problem The problem states that five crates hold 20 pounds of materials, and Jen set up the proportion 20 5 = x 1 to find how many pounds one crate holds. We need to determine the next step in solving this proportion.
Cross-Multiplication To solve the proportion 20 5 = x 1 , we can use cross-multiplication. This involves multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction.
Applying Cross-Multiplication Cross-multiplying gives us 5 ⋅ x = 20 ⋅ 1 , which simplifies to 5 x = 20 .
Identifying the Correct Option Now, we compare this result with the given options:
Cross multiply, 5 x = 20 (This matches our result)
Add across, 6 = 20 x
Cross add, 5 + x = 21
Multiply across, 5 = 20 x The correct option is 'Cross multiply, 5 x = 20 '.
Final Answer The next step to solve the problem is to cross multiply, which results in the equation 5 x = 20 .
Examples
Understanding proportions is crucial in everyday life. For instance, if you're baking a cake and the recipe calls for 2 cups of flour for 8 servings, you can use a proportion to determine how much flour you need for 12 servings. Setting up the proportion 8 2 = 12 x and solving for x will tell you exactly how many cups of flour are needed. This same principle applies to scaling recipes, calculating distances on maps, and determining unit prices while shopping.
