Question

question 2
christian sets aside $60 per month for daily coffee.
mcdonalds sells coffee for $1, and the bean sprout sells a cup of coffee for $3.
a. create an equation that represents the combinations of coffee options that allow christian to stay in his budget
b. graph the equation for his budget.
c. provide 2 combinations that use his entire budget, 1 combination that would be under budget, and 1 combination that would be over his budget.
answer
part a

part b:

part c:

Explanation:

Step1: Define variables and budget inequality

Let $x$ = number of McDonald's coffees ($\$1$ each), $y$ = number of The Bean Sprout coffees ($\$3$ each). Total cost ≤ $\$60$.
$\boldsymbol{x + 3y \leq 60}$
For exact budget use equality: $x + 3y = 60$

Step2: Find intercepts for graph

Set $x=0$ to find y-intercept:
$0 + 3y = 60 \implies y = 20$
Set $y=0$ to find x-intercept:
$x + 3(0) = 60 \implies x = 60$

Step3: Identify valid combinations

• Exact budget: Solve $x + 3y = 60$ for integer pairs.

1. $y=10$: $x=60-3(10)=30$
2. $y=15$: $x=60-3(15)=15$

• Under budget: Choose pair where $x+3y <60$.

$x=10, y=10$: $10+3(10)=40 <60$

• Over budget: Choose pair where $x+3y >60$.

$x=50, y=10$: $50+3(10)=80 >60$

Answer:

Part a:

$\boldsymbol{x + 3y \leq 60}$
(where $x$ = number of $\$1$ McDonald's coffees, $y$ = number of $\$3$ The Bean Sprout coffees)

Part b:

1. Plot the points $(0, 20)$ (y-intercept) and $(60, 0)$ (x-intercept) on the grid.
2. Draw a solid straight line connecting these two points.
3. Shade the region below the line (including the line itself) to represent all combinations within the budget.

Part c:

• Exact budget combinations: (30 McDonald's, 10 The Bean Sprout), (15 McDonald's, 15 The Bean Sprout)
• Under budget combination: (10 McDonald's, 10 The Bean Sprout)
• Over budget combination: (50 McDonald's, 10 The Bean Sprout)