use an equation to solve each problem.\n11. the sum of three consecutive odd integers is 87. find the…
use an equation to solve each problem.\n11. the sum of three consecutive odd integers is 87. find the integers.\n12. the sum of three consecutive odd integers is - 57. find the integers.\n13. three times the sum of a number and twelve is 21. find the number.\n14. five times the difference between a number and 7 is 20. find the number.\n15. 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?\n16. 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?
Answer
11.
Explanation:
Step1: Let the first odd integer be $x$
The next 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
$x+(x + 2)+(x + 4)=3x+6$. So, $3x+6 = 87$.
Step3: Solve for $x$
Subtract 6 from both sides: $3x=87 - 6=81$. Then divide both sides by 3, $x = 27$. The integers are $x=27$, $x + 2=29$, $x + 4=31$.
Answer:
27, 29, 31
12.
Explanation:
Step1: Let the first odd integer be $x$
The next 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
$x+(x + 2)+(x + 4)=3x+6$. So, $3x+6=-57$.
Step3: Solve for $x$
Subtract 6 from both sides: $3x=-57 - 6=-63$. Then divide both sides by 3, $x=-21$. The integers are $x=-21$, $x + 2=-19$, $x + 4=-17$.
Answer:
-21, -19, -17
13.
Explanation:
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:
-5
14.
Explanation:
Step1: Let the number be $x$
The equation is $5(x - 7)=20$.
Step2: Divide both sides by 5
$x - 7=\frac{20}{5}=4$.
Step3: Solve for $x$
Add 7 to both sides: $x=4 + 7=11$.
Answer:
11
15.
Explanation:
Step1: Let the number of days be $d$
The initial amount is 320, the amount spent per day is 6.75, and the final amount is 23. The equation is $320-6.75d=23$.
Step2: Subtract 320 from both sides
$-6.75d=23 - 320=-297$.
Step3: Solve for $d$
Divide both sides by - 6.75: $d=\frac{-297}{-6.75}=44$.
Answer:
44
16.
Explanation:
Step1: Let the length of the shortest side be $x$ inches
The longest side is $2x$ inches, and the other side is 25 inches. The perimeter equation is $x+2x + 25=70$.
Step2: Combine like - terms
$3x+25=70$.
Step3: Subtract 25 from both sides
$3x=70 - 25=45$.
Step4: Solve for $x$
Divide both sides by 3: $x = 15$. The longest side is $2x=30$ inches and the shortest side is $x = 15$ inches.
Answer:
Longest side: 30 inches, Shortest side: 15 inches