Question

use an equation to solve each problem.

1. the sum of three consecutive odd integers is 87. find the integers.
2. the sum of three consecutive odd integers is - 57. find the integers.
3. three times the sum of a number and twelve is 21. find the number.
4. five times the difference between a number and 7 is 20. find the number.
5. sarah has $320 in her bank account. if she spends $6.75 a day on lunch and doesnt earn any money, after how many days will her account be down to $23?
6. the longest side of a triangle is twice as long as the shortest side and the other side is 25 inches. if the perimeter of the triangle is 70 inches, what are the lengths of the longest and shortest sides?

Explanation:

11.

Step1: Let the first odd integer be $x$.

The next two consecutive odd integers are $x + 2$ and $x+4$. The sum equation is $x+(x + 2)+(x + 4)=87$.

Step2: Simplify the left - hand side of the equation.

$x+x + 2+x + 4=3x+6$. So, $3x+6 = 87$.

Step3: Solve for $x$.

Subtract 6 from both sides: $3x=87 - 6=81$. Then divide both sides by 3, $x=\frac{81}{3}=27$.

Step4: Find the other two integers.

$x + 2=27+2 = 29$, $x + 4=27+4=31$.

Step1: Let the first odd integer be $x$.

The next two consecutive odd integers are $x + 2$ and $x+4$. The sum equation is $x+(x + 2)+(x + 4)=-57$.

Step2: Simplify the left - hand side of the equation.

$x+x + 2+x + 4=3x+6$. So, $3x+6=-57$.

Step3: Solve for $x$.

Subtract 6 from both sides: $3x=-57 - 6=-63$. Then divide both sides by 3, $x=\frac{-63}{3}=-21$.

Step4: Find the other two integers.

$x + 2=-21+2=-19$, $x + 4=-21+4=-17$.

Step1: Let the number be $x$.

The equation is $3(x + 12)=21$.

Step2: Divide both sides by 3.

$x+12=\frac{21}{3}=7$.

Step3: Solve for $x$.

Subtract 12 from both sides: $x=7 - 12=-5$.

Answer:

The integers are 27, 29, 31.

12.