Question

Write an equation in each sentence. Analyze and solve. 1. A number decreased by 12 is 8. Find the number2. The product of 8 times a number is 56. Find the number.3. Find three consecutive integers whose sum is 99. Find the integers.

Answer 1

Explanation

1.

$x-12=8$

Adding 12 to both sides we get:

$\begin{gathered} x-12+12=8+12 \\ x=20 \end{gathered}$

2.

$8x=56$

Dividing both sides by 8 we get:

$\begin{gathered} \frac{8x}{8}=\frac{56}{8} \\ x=7 \end{gathered}$

3.

If x is the least, then its consecutive is x+1, we have:

$\begin{gathered} x+x+1=99 \\ \end{gathered}$$2x+1=99$

Subtracting one from both sides we have:

$\begin{gathered} 2x+1-1=99-1 \\ 2x=98 \end{gathered}$

Dividing by two on both sides we get:

$\begin{gathered} \frac{2x}{x}=\frac{98}{2} \\ x=49 \end{gathered}$

The numbers are 49 and 50.