Part A
Jacob has $45.
Muffins costs $0.75 each.
Divide the values to get 45/(0.75) = 60
Answer: 60 muffins maximum
Note: this of course means Jacob cannot buy any doughnuts.
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Part B
Follow the same idea as the previous part.
This time we divide 45 over 0.25
45/(0.25) = 180
Answer: 180 doughnuts maximum
Jacob cannot buy any muffins in this scenario.
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Part C
x = number of muffins
y = number of doughnuts
These are nonnegative whole numbers.
Muffins are $0.75 each.
Buying x of them costs a subtotal of 0.75x dollars.
Doughnuts are $0.25 each.
Buying y of them costs a subtotal of 0.25y dollars.
The grand total is 0.75x+0.25y dollars
Assuming Jacob spends all of the $45, then we set the grand total algebraic expression equal to the 45.
Answer: 0.75x+0.25y = 45
Side note: The equation in red is equivalent to y = -3x+180
I'll stick with the previous version because it shows the 0.75 and 0.25 to help show how each piece contributes to the total.
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Part D
x = number of muffins
y = number of doughnuts
From part A, we found that Jacob can buy 60 muffins and 0 doughnuts. This leads to one ordered pair point of (x,y) = (60,0)
In part B, we found that he can buy 0 muffins and 180 doughnuts. This produces the point (0, 180)
Plot the two points (60,0) and (0,180) and draw a straight line through them. I'll let you check that they work with the equation 0.75x+0.25y = 45 found in part C.
To find other points, follow these steps:
1) Pick any whole number between 1 and 59.
2) Replace x with that value.
3) Solve for y.
At minimum, you only need 2 points to form any straight line.
Answer:
I used GeoGebra to make the graph.