Question 1195743: Jacob has $45 to buy muffins and doughnuts at the school bake sale. Muffins are $0.75 each and doughnuts are $0.25 cents each.
a. What is the maximum number of muffins Jacob can buy?
b. What is the maximum number of doughnuts Jacob can buy?
c. Write an equation that models Jacob's options (assuming he spends all $45)
d. Graph the possible combinations of doughnuts and muffins Jacob can buy for $45.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
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.
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