Question

Write a number in each blank to make the statements true.

Six pencils are equal in value to two rulers.

One ruler is equal in value to two erasers.


Twelve pencils are equal in value to a0 erasers.

Two erasers are equal in value to a1 pencils.

One ruler and four erasers equal the value of a2 pencils.

Answer 1

Explanation:

Let

p = number of pencil

r = number of ruler

e = Number of eraser

Six pencils are equal in value to two rulers.

6p = 2r

Divide both sides by 2 to get r

r = 6p / 2

= 3p

r = 3p

One ruler is equal in value to two erasers.

r = 2e

Recall r = 3p

Therefore, r = 3p = 2e

Twelve pencils are equal in value to a0 erasers.

3p = 2e

To get 12 pencils, multiply both sides by 4

4(3p) = 4(2e)

12p = 8e

12 pencils = 8 erasers

b. 2 erasers are equal to a1 pencils

Recall,

3p = 2e

2 erasers are equal to 3 pencils

c. 1 ruler and 4 erasers are equal to a2 pencils

3p = r = 2e

r + 4e

Multiply 2e by 2 to get 4erasers

= 3p + 2(2e)

Recall, 2e = 3p

= 3p + 2(3p)

= 3p + 6p

= 9p

1 ruler and 4 erasers = 9 pencils