Problem Solving
Translate each statement into an equation, letting ‘the number’ be $x$.
For example:
“When a number is doubled and subtracted from 5, the result is 9” $\quad \boxed{5-2x=9}$
The sum of a number and 11 is 23.
The product of 9 and a number is 72.
If a number is multiplied by 3, and 5 is added to the product, the result is 17.
When a number is decreased by 1 and the resulting number is halved, the answer is 45.
The result of adding 12 to a number is the same as multiplying the number by 4.
If the sum of a number and 4 is tripled, the answer is equivalent to double the number.
Consecutive Numbers
Consecutive numbers are integers in a row.
For example:
- $3, 4, 5$ are consecutive
- $27, 28, 29, 30, 31$ are consecutive
- $13, 15, 17, 19$ are consecutive odd numbers
- $36, 38, 40, 42, 44, 46$ are consecutive even numbers
If $x$ is a number, the next consecutive number is $x+$
and the following consecutive number is
.
If there are three consecutive odd integers and the first number is $x$, the next odd integer is
and the following consecutive odd integer is
.
Translate each statement into an equation, letting ‘the first number’ be $x$.
For example:
“The sum of three consecutive numbers is 24” $\quad \boxed{x+\left(x+1\right)+\left(x+2\right)=24}$
The sum of two consecutive integers is 9.
The sum of three consecutive integers is 51.
The sum of three consecutive odd numbers is 33
The sum of four consecutive even numbers is 100