January 22, 2023 / By Shalini K
*Go through the Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.7 Problem Solvingand get the proper assistance needed during your homework.
Spectrum Math Grade 6 Chapter 5 Lesson 5.7 Problem Solving Answers Key
Write an equation to represent the problem, using the variable n for the unknown number. Then, solve for the value of the variable. Look at the following problem as an example.
Hanna bought some peaches. Kevin bought 12 peaches. He bought 2 times as many as Hanna. How many did Hanna buy?
What is the unknown number? the number of peaches Hanna bought
If n stands for that, what stands for the number of peaches Kevin bought? 2n
What number is that? 12
Equation: 2n = 12 n = 6
Solve each equation.
Question 1.
Joden has a number of baseball cards. He has 35 more than his brother, who has 52. How many cards does Joden have?
What is the unknown number? ____________
Equation: ______ n = __________
Answer:
Number of baseball cards joden contain (j) = 35 more than his brother
Number of baseball cards Joden brother contain (b) = 52
Number of cards that joden have (n)= ?
Equation : n = j + b
n = j + b
n = 87
Therefore Joden contain 87 baseball cards.
Question 2.
Orlando paid $55.60 for a number of tickets to a hockey game. If each ticket was $6.95, how many tickets did Orlando buy?
What is the unknown number? ________________________
Equation: _________________ n = ____________
Answer:
Amount paid to buy a number of tickets for hockey game = $55.60
Amount paid for each ticket (n) = $6.95
Equation: $55.60 ÷ $6.95 = n
55.60 / 6.95= n
n = 8
Therefore Orlando buy’s 8 tickets to the hockey game.
Question 3.
Erica’s room is 1.5 times longer than it is wide. It is 18 feet long. How wide is it?
What is the unknown number? ________________________
Equation: _________________ n = ___________
Answer:
Given Length of Erica’s room = 18 feet
Equation: 1.5 times of Width = 18
This implies width = 18 / 1.5
W = 12
Therefore , the Width of room = 12 feet.
Question 4.
In a recent basketball game, the Grizzlies lost by 11 points. The Palominos beat them with a score of 92 points. How many points did the Grizzlies score?
What is the unknown number? _________________________
Equation: ________________ n = __________
Answer:
Number of points lost by Grizzlies = 11
Number of points beat by Palominos = 92
Number of points scored by Grizzlies (n) = ?
Equation: 92 – n = 11
– n = 11 – 92
– n = – 81
n = 81
Therefore Grizzlies scores 81 points.
Solve each problem.
Question 1.
Martha bought a soft drink for $3.00 and four candy bars. She spent a total of $11.00. How much did each
candy bar cost?
What is the unknown number? ___________________
Equation: __________________ n = ________________
Answer:
suppose, the Cost of every candy bar = C
Number of candy bars = 4
Amount of soft candy = $3.00
Total amount spent on soft drink and candy = $11.00
Cost of each candy bars = ?
Equation: 3 + 4c = 11
4c = 11 – 3
4c = 8
c = 8 / 4
c = 2
Cost of each candy bar (n) = 2
Question 2.
28 students went on a trip to the zoo. All 6 buses were filled and 8 students had to travel in cars. How many students were in each bus?
What is the unknown number? ____________________
Equation: __________________ n = ________________
Answer:
Total Number of students = 28
Number of buses (n)= 6
Number of students to travel in car = 8
Number of students in each bus = ?
Equation: 28 = 6n + 8
6n + 8 – 28 = 0
6n – 20 = 0
6n = 20
n = 20 / 6
n = 3.33
Therefore , around 3 students are there in each bus.
Question 3.
Todd sold half of his comic books and then bought 6 more. He now has I 6. How many did he begin with?
What is the unknown number?
Equation: __________________ n = __________
Answer:
Let the number of comic books = n
half of comic books sold by Todd= n / 2
Number of more books he bought = 6
Number of books Todd is having = 16
Equation: n / 2 + 6 = 16
n / 2 = 16 – 2
n / 2 = 14
n = 28
Therefore, he gin with the number 16.
Question 4.
A bike shop charges $12.00, plus $6.00 an hour for renting a bike. Mike paid $‘+8.00 to rent a bike. How many hours did he pay to have the bike checked out?
What is the unknown number? ___________________
Equation: ___________________ _________________
Answer:
Let the unknown number be ‘ n ‘ the number of hours paid
Amount paid by Mike for rent a bike = $8.00
Amount charged by bike shop for rent= $12.00 + 6.00 for an hour
Number of hours paid for bike to check out (n) = ?
Equation: 12 + 6n = 8
12 + 6n – 8 = 0
6n + 4 = 0
6n = – 4
n = – 4 / 6
n = – 2 / 3
Therefore Mike paid 2/3 amount for check out.
Question 5.
Susan spent $8 of her allowance going to the movies. She gave the dog a bath and earned $5.00. What is
her weekly allowance if she ended up with $20.00?
What is the unknown number? ____________________
Equation: __________________ n = ___________
Answer:
Amount spent by Susan going to movies = $8.00
Amount of money Susan earned = $5.00
Amount of Allowance ended up by Susan =$ 20.00
Amount of Weekly allowances = n = ?
Equation : Ended up = Allowance (n) – Earned + Spent
20 = Allowance(n) – 8 + 5
20 = Allowance(n) – 3
Allowance (n)= 20 + 3
Allowance (n) = 23
Therefore , Susan’s weekly allowance is $23.00
