To solve the equation [tex]\( \frac{3}{?} = \frac{21}{? + 30} \)[/tex] and find the number that can replace both question marks, follow these steps:
1. Setup the Equation:
- The equation given is [tex]\( \frac{3}{x} = \frac{21}{x + 30} \)[/tex], where [tex]\( x \)[/tex] is the unknown number that needs to replace both question marks.
2. Cross-multiply to Eliminate the Fractions:
- Cross-multiplying both sides of the equation to get rid of the fractions, we get:
[tex]\[
3(x + 30) = 21x
\][/tex]
3. Simplify and Solve for [tex]\( x \)[/tex]:
- Distribute the 3 on the left side of the equation:
[tex]\[
3x + 90 = 21x
\][/tex]
- Move all terms involving [tex]\( x \)[/tex] to one side of the equation by subtracting [tex]\( 3x \)[/tex] from both sides:
[tex]\[
90 = 21x - 3x
\][/tex]
- Simplify the right side:
[tex]\[
90 = 18x
\][/tex]
- Divide both sides by 18 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{90}{18}
\][/tex]
- Simplify the fraction:
[tex]\[
x = 5
\][/tex]
Therefore, the number that can replace both question marks is [tex]\( 5 \)[/tex]. The final solution is:
[tex]\[
\boxed{5}
\][/tex]
