Question

Using the info from the word problem and graph, who can buy a bike first? You or your friend?

Answer 1

Given:

There is a bicycle that is cost $175

There are two friends:

The first has $45 and save $5 each week

So, we have the following equation, let (x) is the number of weeks

`45+5x=175`

Solve the equation to find (x):

`\begin{gathered} 5x=175-45 \\ 5x=130 \\ x=(130)/(5)=26\text{ w}eeks \end{gathered}`

So, the first can buy the bicycle after 26 weeks

The second friend has an amount (y) after (x) weeks according to the shown graph of the line:

As shown the line passes through the points (0, 15) and (3, 39)

The slope of the line represents the saving each week =

`slope=(rise)/(run)=(y_2-y_1)/(x_2-x_1)=(39-15)/(3-0)=(24)/(3)=8`

The y-intercept represents the initial saving = $15

So, after (x) week we have the following equation:

`15+8x=175`

Now, solve to find (x)

`\begin{gathered} 8x=175-15 \\ 8x=160 \\ x=(160)/(8)=20 \end{gathered}`

So, the second can buy the bicycle after 20 weeks

So, the answer will be