Question

what x - value makes the set of ratios equivalent?
2 : 3 = 6 : x
4 : 7 = x : 42
2x : 48 = 3 : 12
12 : 15 = x : 20
6
9
16
24

Explanation:

For \(2:3 = 6:x\)

Step1: Cross - multiply the proportion

In a proportion \(a:b = c:d\), we have \(a\times d=b\times c\). So for \(2:3 = 6:x\), we get \(2x = 3\times6\)

Step2: Solve for \(x\)

\(2x=18\), then \(x=\frac{18}{2}=9\)

For \(4:7 = x:42\)

Step1: Cross - multiply the proportion

Using the property \(a:b = c:d\Rightarrow ad = bc\), we have \(4\times42 = 7x\)

Step2: Solve for \(x\)

\(168 = 7x\), then \(x=\frac{168}{7}=24\)

For \(2x:48 = 3:12\)

Step1: Cross - multiply the proportion

From \(a:b = c:d\Rightarrow ad = bc\), we get \(12\times(2x)=48\times3\)

Step2: Solve for \(x\)

\(24x = 144\), then \(x=\frac{144}{24}=6\)

For \(12:15 = x:20\)

Answer:

• For \(2:3 = 6:x\), \(x = 9\)
• For \(4:7 = x:42\), \(x = 24\)
• For \(2x:48 = 3:12\), \(x = 6\)
• For \(12:15 = x:20\), \(x = 16\)

And the matching is: \(6
ightarrow2x:48 = 3:12\), \(9
ightarrow2:3 = 6:x\), \(16
ightarrow12:15 = x:20\), \(24
ightarrow4:7 = x:42\)