Word problem algebra 1 help needed

Question

A store sells gift cards in preset amounts. You can purchase gift cards for $10 or $25. You spent $300 on gift cards. write an equation in standard form to represent the situation. What are 3 combinations of gift cards you could have purchased? 

 

((This is a lesson on standard form and finding x and y intercepts))

I also gave to graph... that's where I'm really stuck

Answer 1

Let's break it down into parts:

Standard Form: Ax+By = C

 

x = the number of $10 cards.

y = the number of $25 cards.

A = 10

B = 25

C = 300

 

So we get this equation:

10x+25y =300

 

Let's find the X and Y-intercept.

 

You buy zero $10 cards:

x=0

25y = 300

y = 300/25 = 12

(0,12): your first combination, which is also your Y-intercept.

 

You buy zero $25 cards:
y=0
10x = 300
x = 300/10 = 30
(30,0): your next combination, which is also your X-intercept.

 

Now we need one more combination, so let's say we buy four $25 cards.

10x + 25(4) = 300 

 

Now solve for X to get your third combination.

(x, 4) 

 

Now you have three different points to make a graph: (0,12), (30,0), and (x,4).

Connect the dots, and that line is your graph. Make sure you label your X-axis and Y-axis. 

Answer 2

10x + 25y = 300, (0, 12), (30, 0)

 

25y = -10x + 300

Pick three values for x and calculate value for y.