Question

A pencil and a ruler cost $1.50 together. The ruler costs $1.00 more than the pencil. How much does the pencil cost?

Answer 1

Answers:

The pencil costs $0.25

The ruler costs $1.25

Step-by-step explanation:

Assume that the cost of the pencil is x and that the cost of the ruler is y.

We are given that:

1- The total cost is $1.5

This means that:

x + y = 1.5 ...........> equation I

2- The ruler costs $1 more than the pencil

This means that:

y = x + 1 ............> equation II

Substitute with equation II in equation I and solve for x as follows:

x + y = 1.5

x + x + 1 = 1.5

2x = 1.5 - 1

2x = 0.5

`x = (0.5)/(2) = 0.25`

This means that:

cost of pencil = x = $0.25

cost of ruler = 1 + 0.25 = $1.25

Hope this helps :)

Answer 2

The pencil costs $0.25.

One way to deduce this is to divide 1.50 by 2 (equaling 0.75) and then subtracting .5 to get 0.25 because if it's $1 more, then the ruler would cost 0.75 + 0.5 and the pencil would cost 0.75 - 0.5, making a total of $1.50.

Another way is to make it an equation. Let's say the ruler is r dollars and the pencil is p dollars.
r + p = 1.50
r = p + 1.00
If we know these two equations, then you can substitute p + 1.00 in the 1st equation (instead of r). This gets us:
p + 1.00 + p = 1.50
You can simplify this into:
2p + 1.00 = 1.50
Then you subtract 1.00 from both sides:
2p = 0.50
And you divide 2 from both sides:
p = 0.25
Getting you the answer of:
The pencil costs $0.25

Hope this helps! :)