Question

check your learning: proportions and cross multiplication
question 1
respond to the following based on your reading.
find the value of x in each of the following proportions.
a. 6 : 9 = x : 72
b. $\frac{8}{3} = \frac{40}{x}$
c. x : 55 = 3 : 5
d. $\frac{33}{x} = \frac{11}{5}$

Explanation:

Part a: \( 6:9 = x:72 \)

Step 1: Cross - multiply

In a proportion \( a:b = c:d \), we have \( ad = bc \). So for \( 6:9 = x:72 \), we get \( 6\times72=9\times x \).
\( 432 = 9x \)

Step 2: Solve for \( x \)

Divide both sides by 9: \( x=\frac{432}{9} = 48 \)

Part b: \( \frac{8}{3}=\frac{40}{x} \)

Step 1: Cross - multiply

Using cross - multiplication for the proportion \( \frac{a}{b}=\frac{c}{d}\) (i.e., \( ad = bc \)), we have \( 8\times x=3\times40 \).
\( 8x = 120 \)

Step 2: Solve for \( x \)

Divide both sides by 8: \( x=\frac{120}{8}=15 \)

Part c: \( x:55 = 3:5 \)

Step 1: Cross - multiply

For the proportion \( a:b = c:d \), \( ad = bc \). So \( x\times5 = 55\times3 \).
\( 5x=165 \)

Step 2: Solve for \( x \)

Divide both sides by 5: \( x = \frac{165}{5}=33 \)

Part d: \( \frac{33}{x}=\frac{11}{5} \)

Answer:

s:
a. \( \boldsymbol{48} \)

b. \( \boldsymbol{15} \)

c. \( \boldsymbol{33} \)

d. \( \boldsymbol{15} \)