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

Dannia Yancy · Accepted Answer

Final Answer : E, Explanation :   First, let's denote the price of a melon as   M M 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 × 8 + 10 M = Natalie’s income 9 	imes 8 + 10M = 	ext{Natalie ' s income} 9 × 8 + 10 M = Natalie’s income  2. For 3 breadfruits and 12 melons:   3 × 8 + 12 M = Natalie’s income 3 	imes 8 + 12M = 	ext{Natalie ' s income} 3 × 8 + 12 M = Natalie’s income  From equation 1:   72 + 10 M = Natalie’s income 72 + 10M = 	ext{Natalie ' s income} 72 + 10 M = Natalie’s income  From equation 2:   24 + 12 M = Natalie’s income 24 + 12M = 	ext{Natalie ' s income} 24 + 12 M = Natalie’s income  Setting the two expressions for Natalie's income equal to each other gives us:  72 + 10 M = 24 + 12 M 72 + 10M = 24 + 12M 72 + 10 M = 24 + 12 M  Solving for   M M M  , we get:  48 = 2 M 48 = 2M 48 = 2 M M = 24 M = 24 M = 24  Substituting   M = 24 M = 24 M = 24   back into either equation to find Natalie's income, we use equation 1:  72 + 10 × 24 = Natalie’s income 72 + 10 	imes 24 = 	ext{Natalie ' s income} 72 + 10 × 24 = Natalie’s income 72 + 240 = 312 72 + 240 = 312 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.

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