Question

A Website sells MP3 downloads of music for $10 and Blu-ray discs of movies for $30. Fiona wants to buy some albums and some movies. She plans to spend a total of $150. Write and graph an equation to represent the situation.

How do i work this out?

Answer 1

x + 3y = 15

The graph is attached below.

Explanation:

Given the price of album = $10.

and the price of movies = $30.

Let's assume she buys "X" albums and "Y" movies.

Cost would be (10X + 30Y).

She plans to spend a total of $150, so cost would be same as total expenditure.

10X + 30Y = 150

X + 3Y = 15

we can graph this equation of line on a graph paper as given below:-

Answer 2

Let x be the number of albums to be bought and

let y be the number of movies to be bought.

The amount to be spent on albums is 10x and

The amount to be spent on movies is 30y.

As per the given condition: The total amout to be spent must equal $ 150.

then, we have

`10x+30y = 150` ......[1]

Now, find x-intercepts and y-intercepts of equation [1];

x-intercepts defined as the graph crosses the x-axis.

Substitute y= 0 in [1] to solve for x;

`10x+30(0)=150`

10x =150

Divide both sides by 10 we get;

`(10x)/(10)=(150)/(10)`

Simplify:

x = 15

y-intercepts defined as the graph crosses the y-axis.

Substitute value of x=0 in [1] to solve for y;

10(0)+30y = 150

30y =150

Divide both sides by 30 we get;

y =5

Now, plot these points (0, 5) and (15, 0) on graph and connect them with a line as shown in the figure below;