Math in Focus Grade 5 Chapter 5 Answer Key Algebra

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 5 Algebra to finish your assignments.

Math in Focus Grade 5 Chapter 5 Answer Key Algebra

Math Journal

John’s solutions to the following problems are as shown. Identify and explain the mistakes John has made. Then give the correct solution.

Question 1.
4w + 12w – 10 = 16w – 10
= 6 w
Answer:
4w + 12w – 10 = 16w – 10
Explanation:
John has made a mistake in subtracting number from a variable type of number. So, the correct solution is 16w – 10.

Question 2.
20p – 2p + 4p = 20p – 6 p
= 14p
Answer:
20p – 2p + 4p = 24p – 2p = 22p
Explanation:
John has made a mistake in the order of subtraction and additions. First we should add all the numbers and then subtract the numbers. So, the correct solution is 22p.

Question 3.
6 ÷ q = \(\frac{q}{6}\)
Answer:
6 ÷ q = 6/q
Explanation:
John has made a mistake in putting the numerator and denominator of a division.
The number before the division symbol (÷) should be consider as numerator.
The number after the division symbol (÷) should be consider as denominator.
So, the correct solution is 6/q.

Question 4.
Clarissa bought 3 cartons of milk for y cents each. She gave the cashier $10. How much change did she receive? Express your answer in terms of y.
Answer:
3 × y = 3y
3 cartons of milk cost 3y cents.
$1 = 100 cents
So, $10 = 1,000 cents
Hence, Clarissa received (1,000 – 3y) cents in change.

Put On Your Thinking Cap!

Challenging Practice

Wendy bought 7 handbags. Each handbag costs the same amount. She paid the cashier $100 and received g dollars in change.

a. What was the cost of each handbag in terms of g?
Answer:
Total money paid to cashier is $100.
Total number of handbags bought = 7
Total change received = g $
So, cost of 7 handbags = (100-g)$
Cost of each handbag = (100-g)/7 $

b. If the price of each handbag was more than $1 0, what is the least possible value of g? (Assume that the cost of each handbag is a whole number.)
Answer:
Assume that each handbag costs 10$, then change given is (100-(7×10)) =(100-70)$ = 30$
Assume that each handbag costs 12$, then change given is (100-(7×12)) =(100-84)$ = 16$
Assume that each handbag costs 14$, then change given is (100-(7×14)) =(100-98)$ = 2$
So, the least possible value of g is 2.

Put On Your Thinking Cap

Problem Solving

There are 40 pupils in a class. There are x more girls than boys.

a. How many boys are there in terms of x?
Answer:
Let’s say total number of boys are ‘b’.
Then total number of girls in class will be ‘b+x’
Total number of pupils in class = number of boys + number of girls
40 = b + (b+x).
So, b=(40-x)/2
The number of boys in class un terms of ‘x’ is (40-x)/2

b. If x = 4, how many boys are there?
Answer:
As we know that number of boys = (40-x)/2
So, number of boys = (40-4)/2 = 36/2 =18
Therefore, total number of boys in class is 18.

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