Question

Help please

1.) -4(3 + n) > -36

2.) LaTeX: \frac{\left(9+y\right)}{15}>1( 9 + y ) 15 > 1

3. A car rental agency rents cars for $26.20 per day plus $0.35 per mile driven. Your travel budget is $200. Write an inequality that represents the maximum number of miles you can drive during a 1-day rental. Show your work.

4. Suppose that you are running a concession stand when a person gives you $18 and asks for six drinks and as many hot dogs as the remaining money will buy. If drinks are $1.00 and hot dogs are $1.75, what is the maximum number of hot dogs the person can buy? Write an inequality that represents your solution. Show your work.

Answer 1

1. n < 6
2. y > 6
3. 26.20 +0.35m ≤ 200 . . . where m is miles driven
4. 6(1.00) +n(1.75) ≤ 18 . . . . . where n is an integer; maximum n = 6.

Explanation:

1. Divide by -4 and subtract 3:

3 +n < 9 . . . . . . reverse the comparison after division by negative number

n < 6 . . . . . . . . . subtract 3

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2. Multiply by 15 and subtract 9:

9+y > 15

y > 6 . . . . . . . subtract 9

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3. Total charges will be the sum of the per day charge and the product of miles and the per-mile charge. That sum cannot exceed 200:

26.20 + 0.35m ≤ 200 . . . . . where m is miles driven

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4. Total expenses will be the charge for the drinks plus the charge for the hot dogs. Each charge is the product of the price and the number purchased. The total (in dollars) cannot exceed 18.

6(1.00) + n(1.75) ≤ 18

1.75n ≤ 12

n ≤ 6.9 . . . . . divide by 1.75 round to tenths

The maximum number of hot dogs the person can buy is 6.