If she spends all of her income on breadfruits and melons, Natalie can just afford 9 breadfruits and 10 melons per day.She could also use her entire budget to buy 3 breadfruits and 12 melons per day.The price of breadfruits is 8 yen each.How much is Natalie's income per day?
A)313 yen
B)317 yen
C)309 yen
D)303 yen
E)None of the above.

Question

Quizplus · Accepted Answer

First, let's denote the price of a melon as $M$ yen. Given that the price of breadfruits is 8 yen each, we can set up two equations based on the information provided:1. For 9 breadfruits and 10 melons: $9 \times 8 + 10M = \text{Natalie's income}$2. For 3 breadfruits and 12 melons: $3 \times 8 + 12M = \text{Natalie's income}$From equation 1: $72 + 10M = \text{Natalie's income}$From equation 2: $24 + 12M = \text{Natalie's income}$Setting the two expressions for Natalie's income equal to each other gives us:$$72 + 10M = 24 + 12M$$Solving for $M$, we get:$$48 = 2M$$$$M = 24$$Substituting $M = 24$ back into either equation to find Natalie's income, we use equation 1:$$72 + 10 \times 24 = \text{Natalie's income}$$$$72 + 240 = 312$$Therefore, Natalie's income per day is 312 yen, which is not listed among the provided options, making the correct choice "E) None of the above."

If She Spends All of Her Income on Breadfruits and Melons