# REASONING WITH PROPERTIES FROM ALGEBRA WORKSHEET

## About "Reasoning with properties from algebra worksheet"

Reasoning with properties from algebra worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on reasoning properties from algebra.

## Reasoning with properties from algebra worksheet - Problems

Problem 1 :

Solve 7x - 2  =  4x + 9 and write a reason for each step.

Problem 2 :

Solve 52y - 3(12 + 9y)  =  64 and write a reason for each step.

Problem 3 :

When we do exercise every day, we should find our target heart rate. This is the rate at which we achieve an effective workout while not placing too much strain on our heart. Our target heart rate r (in beats per minute) can be determined from our age a (in years) using the equation a = 220 - 10r/7.

(i) Solve the formula for r and write a reason for each step.

(ii) Use the result to find the target heart rate for a 16 year old.

(iii) Find the target heart rate for the following ages :

20, 30, 40, 50 and 60

What happens to the target heart rate as a person gets older ?

Problem 4 :

In the diagram above, AB  =  CD. Prove AC  =  BD.

## Reasoning with properties from algebra worksheet - Solution

Problem 1 :

Solve 7x - 2  =  4x + 9 and write a reason for each step.

Solution :

Given :

7x - 2  =  4x + 13

Subtract property of equality :

Subtract 4x from each side.

3x - 2  =  13

3x  =  15

Division property of equality :

Divide both sides by 2.

x  =  5

Problem 2 :

Solve 52y - 3(12 + 9y)  =  64 and write a reason for each step.

Solution :

Given :

52y - 3(12 + 9y)  =  64

Distributive Property :

Distribute 3 to 12 and 9y.

52y - 36 - 27y  =  64

Simplify :

25y - 36  =  64

25y  =  100

Division property of equality :

Divide both sides by 25.

y  =  4

Problem 3 :

When we do exercise every day, we should find our target heart rate. This is the rate at which we achieve an effective workout while not placing too much strain on our heart. Our target heart rate r (in beats per minute) can be determined from our age a (in years) using the equation a = 220 - 10r/7.

(i) Solve the formula for r and write a reason for each step.

(ii) Use the result to find the target heart rate for a 16 year old.

(iii) Find the target heart rate for the following ages :

20, 30, 40, 50 and 60

What happens to the target heart rate as a person gets older ?

Solution (i) :

Given :

a = 220 - 10r/7

a + 10r/7  =  220

Subtraction property of equality :

Subtract a from each side.

10r/7  =  220 - a

Multiplication property of equality :

Multiply both sides by 7/10.

r  =  7/10 ⋅ (220 - a)

Solution (ii) :

To find the target heart rate for a 16 year old, substitute a = 16.

r  =  7/10 ⋅ (220 - 16)

Simplify :

r  =  7/10 ⋅ 204

r  =  1428 / 10

r  =  142.8

The target hear rate for a 16 year old is about 142.8 beats per minute.

Solution (ii) :

To find the target heart rate for a 16 year old, substitute a = 16.

r  =  7/10 ⋅ (220 - 16)

Simplify :

r  =  7/10 ⋅ 204

r  =  1428 / 10

r  =  142.8

The target hear rate for a 16 year old is about 142.8 beats per minute.

Solution (iii) :

The table given below shows the heart rate for ages 20, 30, 40, 50 and 60.

From the above table, it is clear that the target heart rate appears to decrease as a person gets older.

Problem 4 :

In the diagram above, AB  =  CD. Prove AC  =  BD.

Solution :

Given :

AB  =  CD

AB + BC  =  CD + BC

AB + BC  =  BC + CD ------(1)

By segment addition postulate, we have

AC  =  AB + BC -----(2)

BD  =  BC + CD -----(3)

Substitute (2) and (3) in (1).

(1) -----> AC  =  BD

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