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):

$\begin{gathered} 5x=175-45 \\ 5x=130 \\ x=\frac{130}{5}=26\text{ w}eeks \end{gathered}$

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 =

$slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{39-15}{3-0}=\frac{24}{3}=8$

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)

$\begin{gathered} 8x=175-15 \\ 8x=160 \\ x=\frac{160}{8}=20 \end{gathered}$

So, the second can buy the bicycle after 20 weeks

So, the answer will be