Question

directions: solve each problem using the 3 - step process.

1. the larger of two numbers is 12 more than the smaller number. if the sum of the two numbers is 74, find the two numbers.
2. the larger of two numbers is 10 less than twice the smaller number. if the sum of the two numbers is 38, find the two numbers.
3. the number of years that brad has been on the soccer team is 2 less than 5 times the number of years that scott has. in total, the boys have been on the soccer team for 10 years. how long has brad been on the soccer team?
4. there are 10 less trumpet players than saxophone players. the number of saxophone players is 3 times the number of trumpet players. how many trumpet players are there?
5. the length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches, find the dimensions of the rectangle.
6. the length of a rectangle is 4 centimeters more than twice its width. if the perimeter of the rectangle is 86 centimeters, find the dimensions of the rectangle.

Explanation:

1.

Step1: Let variables

Let the smaller number be $x$, then the larger number is $x + 12$.

Step2: Set up equation

The sum of the two - numbers is 74, so $x+(x + 12)=74$.
Simplify the left - hand side: $2x+12 = 74$.
Subtract 12 from both sides: $2x=74 - 12=62$.
Divide both sides by 2: $x = 31$.

Step3: Find the larger number

The larger number is $x + 12=31+12 = 43$.

Step1: Let variables

Let the smaller number be $x$, then the larger number is $2x-10$.

Step2: Set up equation

The sum of the two numbers is 38, so $x+(2x - 10)=38$.
Simplify the left - hand side: $3x-10 = 38$.
Add 10 to both sides: $3x=38 + 10=48$.
Divide both sides by 3: $x = 16$.

Step3: Find the larger number

The larger number is $2x-10=2\times16-10=32 - 10=22$.

Step1: Let variables

Let the number of years Scott has been on the team be $x$, then the number of years Brad has been on the team is $5x-2$.

Step2: Set up equation

The total number of years they have been on the team is 10, so $x+(5x - 2)=10$.
Simplify the left - hand side: $6x-2 = 10$.
Add 2 to both sides: $6x=10 + 2=12$.
Divide both sides by 6: $x = 2$.

Step3: Find Brad's years

Brad has been on the team for $5x-2=5\times2-2=10 - 2 = 8$ years.

Answer:

The two numbers are 31 and 43.

2.