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Juan chooses 4 items for his main course, 1 drink, and 1 dessert in a restaurant. The total cost of the meal is $9.80. Each main course item costs $1.10 and the dessert costs 50¢ more than the drink.

Let d represent Juan's dessert and r represent his drink.

Select True or False for each statement

Juan chooses 4 items for his main course 1 drink and 1 dessert in a restaurant The total cost of the meal is 980 Each main course item costs 110 and the dessert class=

Respuesta :

Answers:

  • A) True
  • B) False
  • C) False
  • D) True
  • E) True

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Explanation:

The two items given

  • "Juan choses 4 items for his main course"
  • "each main course item costs $1.10"

tells us that he spends 4*1.10 dollars on just the main course items. So that's why choice A is true.

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From part A, we know that Juan spends 4*1.10 = 4.40 dollars on just the main course items. We also know the total cost of the meal is $9.80

This leaves 9.80 - 4.40 = 5.40 left over

Meaning that $5.40 is spent on dessert and drinks

The equation in part B is close, but the 4.40 should be 5.40 instead.

Choice B is false

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"The dessert costs 50 cents more than the drink" means

r = d+0.50

Whatever the drink costs (d), we add on 50 cents or $0.50 to get the cost of the dessert (r). This is why choice C is false.

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The system of equations we have so far is

[tex]\begin{cases}5.40 = d+r\\r = d+0.50\end{cases}[/tex]

Start with the first equation, plug in r = d+0.50, and solve for d

5.40 = d+r

5.40 = d+d+0.50

5.40 = 2d+0.50

2d+0.50 = 5.40

2d = 5.40-0.50

2d = 4.90

d = 4.90/2

d = 2.45

Each drink costs $2.45, so choice D is true because Juan only bought one drink.

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Lets use this value of d to find r

r = d+0.50

r = 2.45+0.50

r = 2.95

Each dessert costs $2.95, making choice E true as well (since he only bought one dessert).

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