Answers

Example 6.40

Solution
ⓐ  
  3 is to 7 as 15 is to 35 .
Write as a proportion. \dfrac{3}{7}=\dfrac{15}{35}

 

ⓑ  
  5 hits in 8 at-bats is the same as 30 hits in 48 atbats.
Write each fraction to compare hits to at-bats. \dfrac{\text { hits }}{\text { at-bats }}=\dfrac{\text { hits }}{\text { at-bats }}
Write as a proportion. \dfrac{5}{8}=\dfrac{30}{48}

 

ⓒ  
  \$ 1.50 for 6 ounces is equivalent to \$ 2.25 for 9 ounces.
Write each fraction to compare dollars to ounces. \dfrac{\$}{\text { ounces }}=\dfrac{\$}{\text { ounces }}
Write as a proportion. \dfrac{1.50}{6}=\dfrac{2.25}{9}



Example 6.41

Solution

To determine if the equation is a proportion, we find the cross products. If they are equal, the equation is a proportion.

ⓐ  
  \dfrac{4}{9}=\dfrac{12}{28}
Find the cross products. 28 \cdot 4=112
9 \cdot 12=108


Since the cross products are not equal, 28 \cdot 4 \neq 9 \cdot 12, the equation is not a proportion.


ⓑ  
  \dfrac{17.5}{37.5}=\dfrac{7}{15}
Find the cross products. 15 \cdot 17.5=262.5 \quad 37.5 \cdot 7=262.5


Since the cross products are equal, 15 \cdot 17.5=37.5 \cdot 7, the equation is a proportion.


Example 6.42

Solution
  \dfrac{x}{63}=\dfrac{4}{7}
To isolate x, multiply both sides by the LCD, 63. \color{red}{63}\left(\dfrac{x}{63}\right)=\color{red}{63}\left(\dfrac{4}{7}\right)
Simplify. x=\dfrac{9 \cdot \not{7} \cdot 4}{\not{7}}
Divide the common factors. x=36
Check: To check our answer, we substitute into the original proportion.    
  \dfrac{x}{63}=\dfrac{4}{7}  
Substitute x=\color{red}{36} \dfrac{\color{red}{36}}{63} \stackrel{?}{=} \dfrac{4}{7}  
Show common factors. \dfrac{4 \cdot 9}{7 \cdot 9} \stackrel{?}{=} \dfrac{4}{7}  
Simplify. \dfrac{4}{7}=\dfrac{4}{7}✓  



Example 6.43

Solution

Notice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal.

 
Find the cross products and set them equal. 4 \cdot 144=a \cdot 9
Simplify. 576=9 a
Divide both sides by 9. \dfrac{576}{9}=\dfrac{9 a}{9}
Simplify. 64=a
Check your answer.    
  \dfrac{144}{a}=\dfrac{9}{4}  
Substitute a=\color{red}{64} \dfrac{144}{64} \stackrel{?}{=} \dfrac{9}{4}  
Show common factors.. \dfrac{9 \cdot 16}{4 \cdot 16} \stackrel{?}{=} \dfrac{9}{4}  
Simplify. \dfrac{9}{4}=\dfrac{9}{4}✓  


Another method to solve this would be to multiply both sides by the LCD, 4aTry it and verify that you get the same solution.


Example 6.44

Solution
Find the cross products and set them equal.
  y \cdot 52=91(-4)
Simplify. 52 y=-364
Divide both sides by 52. \dfrac{52 y}{52}=\dfrac{-364}{52}
Simplify. y=-7
Check:    
  \dfrac{52}{91}=\dfrac{-4}{y}  
Substitute y=\color{red}{-7} \dfrac{52}{91} \stackrel{?}{=} \dfrac{-4}{\color{red}{-7}}  
Show common factors. \dfrac{13 \cdot 4}{13 \cdot 4} \stackrel{?}{=} \dfrac{-4}{\color{red}{-7}}  
Simplify. \dfrac{4}{7}=\dfrac{4}{7}\checkmark