Here are six numbers. $$ 14 \quad 16 \quad 18 \quad 21 \quad 24 \quad 40 $$ use each of these numbers once to make these statements correct. $$ \begin{array}{ll} ext { a } \frac{2}{3} ext { of } \square 1 \ ext { c } \frac{2}{5} ext { of } 40 & ext { b } \frac{3}{4} ext { of } \square\end{array} $$

Question

Here are six numbers. $$ 14 \quad 16 \quad 18 \quad 21 \quad 24 \quad 40 $$ use each of these numbers once to make these statements correct. $$ \begin{array}{ll}	ext { a } \frac{2}{3} 	ext { of } \square 1 \ 	ext { c } \frac{2}{5} 	ext { of } 40 & 	ext { b } \frac{3}{4} 	ext { of } \square\end{array} $$

UpStudy AI · Accepted Answer

1. We are given the numbers  
   $$ 14,\ 16,\ 18,\ 21,\ 24,\ 40 $$  
   and three equations where each equation must use two of these numbers (one as the number being multiplied and one as the result). The equations are:
   
   - Equation (a):  
     $$
     \frac{2}{3} \text{ of } \square = \square
     $$
     
   - Equation (b):  
     $$
     \frac{3}{4} \text{ of } \square = \square
     $$
     
   - Equation (c):  
     $$
     \frac{2}{5} \text{ of } 40 = \square
     $$
     
   Each of the six given numbers must be used exactly once.

2. **Solve Equation (c):**  
   We compute:
   $$
   \frac{2}{5} \times 40 = \frac{2 \times 40}{5} = \frac{80}{5} = 16.
   $$
   Thus, Equation (c) becomes:
   $$
   \frac{2}{5} \text{ of } 40 = 16.
   $$
   This uses the numbers $$ 40 $$ and $$ 16 $$.

3. **Solve Equation (a):**  
   We have the form:
   $$
   \frac{2}{3} \times x = y,
   $$
   where both $$ x $$ and $$ y $$ must come from the remaining numbers $$ 14,\ 18,\ 21,\ 24 $$.

We want $$ x $$ such that $$\frac{2}{3} x$$ is an integer and is one of the remaining numbers.
   
   Try $$ x = 21 $$:
   $$
   \frac{2}{3} \times 21 = \frac{42}{3} = 14.
   $$
   Since both $$ 21 $$ and $$ 14 $$ are on our list, we take:
   $$
   \frac{2}{3} \text{ of } 21 = 14.
   $$
   This uses the numbers $$ 21 $$ and $$ 14 $$.

4. **Solve Equation (b):**  
   Now the remaining numbers are $$ 18 $$ and $$ 24 $$. Equation (b) is given as:
   $$
   \frac{3}{4} \times z = w.
   $$
   
   Try $$ z = 24 $$:
   $$
   \frac{3}{4} \times 24 = \frac{72}{4} = 18.
   $$
   This works, and we have:
   $$
   \frac{3}{4} \text{ of } 24 = 18.
   $$
   This uses the numbers $$ 24 $$ and $$ 18 $$.

5. **Answer Summary:**

- $$ \frac{2}{3} $$ of $$ 21 $$ is $$ 14 $$.
   - $$ \frac{3}{4} $$ of $$ 24 $$ is $$ 18 $$.
   - $$ \frac{2}{5} $$ of $$ 40 $$ is $$ 16 $$.

All six numbers have been used exactly once.
Here's how to use each number once to make the statements correct: - $$ \frac{2}{3} $$ of 21 is 14. - $$ \frac{3}{4} $$ of 24 is 18. - $$ \frac{2}{5} $$ of 40 is 16. All six numbers are used exactly once.

Here are six numbers.

use each of these numbers once to make these statements correct.

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