QuestionAugust 23, 2025

5. What is the minimum number of 15 accessories and 25 electronics needed to achieve a 400 sales goal? a 15x+25ygeqslant 400 b 5x+15ygeqslant 400 C 15x+25yleqslant 400 15x+25y=400

5. What is the minimum number of 15 accessories and 25 electronics needed to achieve a 400 sales goal? a 15x+25ygeqslant 400 b 5x+15ygeqslant 400 C 15x+25yleqslant 400 15x+25y=400
5. What is the minimum number of 15 accessories and 25 electronics needed to achieve a 400
sales goal?
a 15x+25ygeqslant 400
b 5x+15ygeqslant 400
C 15x+25yleqslant 400
15x+25y=400

Solution
4.4(185 votes)

Answer

10 accessories and 10 electronics (total 20 items) are needed. Explanation 1. Identify the Correct Equation The equation 15x + 25y = 400 represents the exact sales goal of \400 using \15 accessories and \25 electronics. 2. Simplify the Equation Divide the entire equation by 5 to simplify: 3x + 5y = 80. 3. Solve for Integer Solutions Find integer values of x and y that satisfy 3x + 5y = 80. Start with y = 0: 3x = 80, not an integer. Try y = 1: 3x + 5 = 80 \Rightarrow 3x = 75 \Rightarrow x = 25. Check other small values of y until a smaller sum is found. 4. Minimize Total Items For y = 5: 3x + 25 = 80 \Rightarrow 3x = 55 \Rightarrow x = \frac{55}{3}, not an integer. For y = 10: 3x + 50 = 80 \Rightarrow 3x = 30 \Rightarrow x = 10. Total items: x + y = 20.

Explanation

1. Identify the Correct Equation<br /> The equation $15x + 25y = 400$ represents the exact sales goal of \$400 using \$15 accessories and \$25 electronics.<br /><br />2. Simplify the Equation<br /> Divide the entire equation by 5 to simplify: $3x + 5y = 80$.<br /><br />3. Solve for Integer Solutions<br /> Find integer values of $x$ and $y$ that satisfy $3x + 5y = 80$. Start with $y = 0$: $3x = 80$, not an integer. Try $y = 1$: $3x + 5 = 80 \Rightarrow 3x = 75 \Rightarrow x = 25$. Check other small values of $y$ until a smaller sum is found.<br /><br />4. Minimize Total Items<br /> For $y = 5$: $3x + 25 = 80 \Rightarrow 3x = 55 \Rightarrow x = \frac{55}{3}$, not an integer. For $y = 10$: $3x + 50 = 80 \Rightarrow 3x = 30 \Rightarrow x = 10$. Total items: $x + y = 20$.
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