Printable math worksheet featuring 14 problems where students must solve for the unknown variable in equivalent ratio equations.

To solve the problems involving equivalent ratios, we need to use the property that in an equivalent ratio, the cross-products are equal. That is, for a ratio \( a : b = c : d \), we have \( a \cdot d = b \cdot c \).

Let's solve each problem step by step.

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1) \( 16 : 20 = x : 5 \)

Given:
\[ 16 : 20 = x : 5 \]

Using the cross-product property:
\[ 16 \cdot 5 = 20 \cdot x \]

Simplify:
\[ 80 = 20x \]

Solve for \( x \):
\[ x = \frac{80}{20} = 4 \]

Answer:
\[ x = 4 \]

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2) \( 78 : 169 = 12 : y \)

Given:
\[ 78 : 169 = 12 : y \]

Using the cross-product property:
\[ 78 \cdot y = 169 \cdot 12 \]

Simplify:
\[ 78y = 2028 \]

Solve for \( y \):
\[ y = \frac{2028}{78} = 26 \]

Answer:
\[ y = 26 \]

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3) \( 8 : 60 = 4 : p \)

Given:
\[ 8 : 60 = 4 : p \]

Using the cross-product property:
\[ 8 \cdot p = 60 \cdot 4 \]

Simplify:
\[ 8p = 240 \]

Solve for \( p \):
\[ p = \frac{240}{8} = 30 \]

Answer:
\[ p = 30 \]

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4) \( 40 : 16 = l : 22 \)

Given:
\[ 40 : 16 = l : 22 \]

Using the cross-product property:
\[ 40 \cdot 22 = 16 \cdot l \]

Simplify:
\[ 880 = 16l \]

Solve for \( l \):
\[ l = \frac{880}{16} = 55 \]

Answer:
\[ l = 55 \]

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5) \( 56 : 24 = 7 : z \)

Given:
\[ 56 : 24 = 7 : z \]

Using the cross-product property:
\[ 56 \cdot z = 24 \cdot 7 \]

Simplify:
\[ 56z = 168 \]

Solve for \( z \):
\[ z = \frac{168}{56} = 3 \]

Answer:
\[ z = 3 \]

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6) \( q : 2 = 35 : 10 \)

Given:
\[ q : 2 = 35 : 10 \]

Using the cross-product property:
\[ q \cdot 10 = 2 \cdot 35 \]

Simplify:
\[ 10q = 70 \]

Solve for \( q \):
\[ q = \frac{70}{10} = 7 \]

Answer:
\[ q = 7 \]

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7) \( 21 : a = 3 : 4 \)

Given:
\[ 21 : a = 3 : 4 \]

Using the cross-product property:
\[ 21 \cdot 4 = 3 \cdot a \]

Simplify:
\[ 84 = 3a \]

Solve for \( a \):
\[ a = \frac{84}{3} = 28 \]

Answer:
\[ a = 28 \]

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8) \( 3 : c = 27 : 90 \)

Given:
\[ 3 : c = 27 : 90 \]

Using the cross-product property:
\[ 3 \cdot 90 = 27 \cdot c \]

Simplify:
\[ 270 = 27c \]

Solve for \( c \):
\[ c = \frac{270}{27} = 10 \]

Answer:
\[ c = 10 \]

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9) \( 42 : 18 = 35 : d \)

Given:
\[ 42 : 18 = 35 : d \]

Using the cross-product property:
\[ 42 \cdot d = 18 \cdot 35 \]

Simplify:
\[ 42d = 630 \]

Solve for \( d \):
\[ d = \frac{630}{42} = 15 \]

Answer:
\[ d = 15 \]

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10) \( 20 : 150 = s : 30 \)

Given:
\[ 20 : 150 = s : 30 \]

Using the cross-product property:
\[ 20 \cdot 30 = 150 \cdot s \]

Simplify:
\[ 600 = 150s \]

Solve for \( s \):
\[ s = \frac{600}{150} = 4 \]

Answer:
\[ s = 4 \]

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11) \( 48 : e = 20 : 25 \)

Given:
\[ 48 : e = 20 : 25 \]

Using the cross-product property:
\[ 48 \cdot 25 = 20 \cdot e \]

Simplify:
\[ 1200 = 20e \]

Solve for \( e \):
\[ e = \frac{1200}{20} = 60 \]

Answer:
\[ e = 60 \]

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12) \( 4 : 11 = f : 44 \)

Given:
\[ 4 : 11 = f : 44 \]

Using the cross-product property:
\[ 4 \cdot 44 = 11 \cdot f \]

Simplify:
\[ 176 = 11f \]

Solve for \( f \):
\[ f = \frac{176}{11} = 16 \]

Answer:
\[ f = 16 \]

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13) \( e : 10 = 6 : 5 \)

Given:
\[ e : 10 = 6 : 5 \]

Using the cross-product property:
\[ e \cdot 5 = 10 \cdot 6 \]

Simplify:
\[ 5e = 60 \]

Solve for \( e \):
\[ e = \frac{60}{5} = 12 \]

Answer:
\[ e = 12 \]

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14) \( 18 : j = 9 : 7 \)

Given:
\[ 18 : j = 9 : 7 \]

Using the cross-product property:
\[ 18 \cdot 7 = 9 \cdot j \]

Simplify:
\[ 126 = 9j \]

Solve for \( j \):
\[ j = \frac{126}{9} = 14 \]

Answer:
\[ j = 14 \]

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & x = 4 \\
2) & y = 26 \\
3) & p = 30 \\
4) & l = 55 \\
5) & z = 3 \\
6) & q = 7 \\
7) & a = 28 \\
8) & c = 10 \\
9) & d = 15 \\
10) & s = 4 \\
11) & e = 60 \\
12) & f = 16 \\
13) & e = 12 \\
14) & j = 14 \\
\end{array}
}
\]