This handy Spectrum Math Grade 7 Answer Key Chapter 3 Lesson 3.3 Creating Expressions to Solve Problems provides detailed answers for the workbook questions.
Spectrum Math Grade 7 Chapter 3 Lesson 3.3 Creating Expressions to Solve Problems Answers Key
Write expressions to solve problems by putting the unknown number, or variable, on one side of the equation and the known values on the other side of the equation. Then, solve for the value of the variable.
Francine is making earrings and necklaces for six friends. Each pair of earrings uses 6 centimeters of wire and each necklace uses 30 centimeters. How much wire will Francine use?
Let w represent the amount of wire used.
Equation: w = 6 × (6 + 30)
Another way of writing this expression is: w = (6 × 6) + (6 × 30)
How much wire did Francine use? w = 2 16 centimeters
Solve each problem.
Question 1.
A jaguar can run 40 miles per hour while a giraffe can run 32 miles per hour. If they both run for 4 hours, how
much farther will the jaguar run?
Let d represent the distance.
Equation: ________
Another way of writing this is: _________
The jaguar will run ____ miles farther.
Answer: 32
Let d represent the distance.
Equation: 4 x (40 – 32)
Another way of writing this is: d = (4 x 40) – (4 x 32)
Therefore d = (160) – (128)
d = 32
The jaguar will run 32 miles farther.
Question 2.
Charlene sold 15 magazine subscriptions for the school fundraiser. Mark sold 17 subscriptions and Paul sold 12.
How many magazine subscriptions did they sell in all?
Let s represent subscriptions.
Equation: __________
Another way of writing this is: __________
They sold ________ subscriptions in all.
Answer: 44
Let s represent subscriptions.
Equation: 15 + 17 +12
Another way of writing this is: s = 15 + 17 +12
Therefore, s = 44
They sold 44 subscriptions in all.
Question 3.
Shara bought 3 bags of chocolate candies for $ 1.25 each 3. and 3 bags of gummy bears for $2.00 each. How much did she spend in all?
Let m represent the money spent.
Equation: ___________
Another way of writing this is: ____________
Shara spent ______ on candy.
Answer: $ 9.75
Let m represent the money spent.
Equation: 3(1.25) + 3(2.00) = m
Another way of writing this is: m = 3 x (1.25 + 2.00)
Therefore, m = 9.75
Shara spent $ 9.75 on candy.
Solve each problem.
Question 1.
Elsa sold 37 pairs of earrings for $20 each at the craft fair. She is going to use \(\frac{1}{4}\) of the money to buy new CDs and is going to put the rest of the money in her savings account. How much money will she put into her savings account?
Let s stand for the amount of money saved.
Equation: ______________
How much money did she spend on CDs? ______________
How much money did she put in her savings account?
___________________
Answer: 555
Let s stand for the amount of money saved.
Equation: s = (20 x 37) ( 1 – \(\frac{1}{4}\))
Elsa sold 37 pairs of earrings for $20 each at the craft fair
Therefore, Elsa made 20 x 37 = $ 740
She is going to use \(\frac{1}{4}\) of the money to buy new CDs
So, the amount of money she spent on CDs = 740 x \(\frac{1}{4}\) = 185
Therefore, the money she put in her savings account = 740 – 185 = 555
How much money did she spend on CDs? 185
How much money did she put in her savings account?
555
Question 2.
Jason deposits $5 into his savings account twice a week for 6 weeks. How much money will he have saved after 6 weeks?
Let s stand for the amount of money saved.
Equation: ________________
How much money did he save? ___________
Answer: 60
Let s stand for the amount of money saved.
Equation: s = (5 x 2) x 6
Therefore, s = 60
How much money did he save? 60
Question 3.
Four friends went to the movies. Each ticket cost $8 and each person bought popcorn and a soda for $5. How much did they spend in all?
Let m stand for the amount of money spent.
Equation: ____________
What is another way to write the above equation? _________
How much money did they spend? _____________
Answer: 52
Let m stand for the amount of money spent.
Equation: 4 x (8 + 5)
What is another way to write the above equation? m = (4 x 8 ) + (4 x 5)
Therefore, m = 32 + 20
m = 52
How much money did they spend? 52
Question 4.
An online store increased the price of a shirt by 17% and charged $3 to ship the shirt to a customer. The customer paid $43 for the shirt. What was the original price of the shirt?
Let p stand for the price of the shirt.
Equation: ____________
How much was the shirt before the increase and shipping?
_____________
Answer:
Let p stand for the price of the shirt.
Equation: p(1 + \(\frac{17}{100}\)) + 3 = 43
\(\frac{(100 x p) + (17 x p ) + 300}{100}\)) = 43
\(\frac{(100p + 17p + 300}{100}\)) = 43
\(\frac{117p + 300}{100}\)) = 43
117p + 300 = 4300
117p = 4300 – 300
117p = 4000
p = \(\frac{4000}{117}\))
p = 34.19
How much was the shirt before the increase and shipping?
34.19
Question 5.
David and Eric went out to dinner. Their total bill was $45. They added 20% gratuity to the bill. If they split the bill in half, how much did each person spend?
Let t stand for the amount each person spent.
Equation: ____________
How much money did each person spend? _________
Answer: 27
Let t stand for the amount each person spent.
Equation: t = (45 + (45 x 0.2) ) x \(\frac{1}{2}\)
t = (45 + 9) x \(\frac{1}{2}\)
t = 54 x \(\frac{1}{2}\)
t = 27
How much money did each person spend? 27