Question

for problems 1–4, write an expression or equation that represents each description. do not evaluate.

1. 8 more than 22
2. 33 divided by the sum of 8 and 3
3. 10 is 1 more than 3 squared.
4. \\(\frac{3}{4}\\) of 36 is the product of 3 and 9.

for problems 5 and 6, fill in the blank to make a true number sentence.

1. \\(14 - \underline{\quad} = 2^3 + 5\\)
2. \\(\frac{1}{2}(30 - 12) = 5 + \underline{\quad}\\)
3. write a description of \\(n + 5 = 10\\).
4. write a description of \\(\frac{1}{3}x - 2 = 8\\).
5. match each equation with the number that is the solution to the equation.

equation: \\(17n = 51\\), \\(4^2 = n\\), \\(\frac{1}{5}n = 2\\), \\(\frac{n}{3} = 5\\)
number: 10, 15, 3, 16

Explanation:

Step1: Translate "8 more than 22"

$22 + 8$

Step2: Translate "33 divided by sum of 8&3"

$\frac{33}{8+3}$

Step3: Translate "10 is 1 more than 3 squared"

$10 = 3^2 + 1$

Step4: Translate "3/4 of 36 = product of 3&9"

$\frac{3}{4} \times 36 = 3 \times 9$

Step5: Solve for blank in $14 - \square = 2^3+5$

First calculate $2^3+5=8+5=13$, then $\square=14-13=1$

Step6: Solve for blank in $\frac{1}{2}(30-12)=5+\square$

First calculate $\frac{1}{2}(18)=9$, then $\square=9-5=4$

Step7: Describe $n+5=10$

State the verbal form of the equation

Step8: Describe $\frac{1}{3}x-2=8$

State the verbal form of the equation

Step9: Solve each matching equation

1. $17n=51$: $n=\frac{51}{17}=3$
2. $4^2=n$: $n=16$
3. $\frac{1}{5}n=2$: $n=2\times5=10$
4. $\frac{n}{3}=5$: $n=5\times3=15$

Answer:

1. $22 + 8$
2. $\frac{33}{8+3}$
3. $10 = 3^2 + 1$
4. $\frac{3}{4} \times 36 = 3 \times 9$
5. $1$
6. $4$
7. The sum of a number $n$ and 5 equals 10.
8. Two less than one-third of a number $x$ equals 8.

9.

• $17n=51$ matches 3
• $4^2=n$ matches 16
• $\frac{1}{5}n=2$ matches 10
• $\frac{n}{3}=5$ matches 15