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

Step-by-step 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} (8x)/(8)=(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} (2x)/(x)=(98)/(2) \\ x=49 \end{gathered}`

The numbers are 49 and 50.