Question

The replacement set for an equation is {12, 18, 32, 48}. The equation is represented by the sentence, "34 of a number is 24." What is the solution set of the equation? Responses {12} open curly bracket 12 close curly bracket, {18} open curly bracket 18 close curly bracket {32} open curly bracket 32 close curly bracket {48}

Answer 1

Answer:

• The number is 48

Step-by-step explanation:

It is assumed the question is:

• "3/4 of a number is 24, find the number"

Let the number be x.

Set equation:

• x*3/4 = 24
• x = 24 : 3/4
• x = 24 * 4/3
• x = 48

Answer 2

Answer:

{32}

Step-by-step explanation:

The replacement set for an equation is the set of values that may be substituted for the variable.

Let x be the variable.

Given equation:

$\textsf{ \dfrac{3}{4} of a number is 24 \implies \dfrac{3}{4}x=24 }.$

The solution set is the set of all values that make the equation true.

To find the solution set from the replacement set, input each value from the replacement set and evaluate both sides of the equation. If the two sides are equal, the equation is true and the value is a solution.

$\begin{aligned}x=12 \implies \dfrac{3}{4}(12)&=24\\\dfrac{3 \cdot 12}{4}&=24\\\dfrac{36}{4}&=24\\9&=24\end{aligned}$

As 9 ≠ 24, x = 12 is not a solution.

$\begin{aligned}x=18 \implies \dfrac{3}{4}(18)&=24\\\dfrac{3 \cdot 18}{4}&=24\\\dfrac{54}{4}&=24\\13.5&=24\end{aligned}$

As 13.5 ≠ 24, x = 18 is not a solution.

$\begin{aligned}x=32 \implies \dfrac{3}{4}(32)&=24\\\dfrac{3 \cdot 32}{4}&=24\\\dfrac{96}{4}&=24\\24&=24\end{aligned}$

As both sides equal, the equation is true and x = 32 is a solution.

$\begin{aligned}x=48 \implies \dfrac{3}{4}(48)&=24\\\dfrac{3 \cdot 48}{4}&=24\\\dfrac{144}{4}&=24\\36&=24\end{aligned}$

As 36 ≠ 24, x = 48 is not a solution.

Therefore, the solution set is {32}.