1. The cost in dollars of an "n" mile trip with the Supreme Taxi Service is given by 1.5 + 1.75n. The cost of an "n" mile trip using Town Taxi Service is given by 1.9 + 1.6n. For rides between 1 and 10 miles, which service would you choose? Explain.
2. Peach = 35 calories
Banana = 105 calories
Bacon Slice = 37 calories
Bread Slice = 65 calories
Egg = 75 calories
Use this information to write an expression for the number of calories in each situation.
a) "p" peaches and" n" bananas
b) two slices of bread, "b" slices of bacon, and one egg
3. A hot air balloon is at a height of 2,250 feet. It descends 150 feet each minute. Find it's height after six, eight, and ten minutes. Make a table to show the pattern of heights. Write an expression for the balloon's height at "m" minutes.
1. So I assume it's adding 1.5 + 1.75 • n, right? For the first taxi can service? Then, the NEXT one charges 1.9 + 1.6 • n, correct? So far, all I have is that. I don't know what to multiply it by, because it says "between 1 and 10 miles." Would it be n = 5?
2. I think these are the answers, but I'm not sure, so I need some help:
a) p • n (or 35 • 105)
b) 65 • 2 + b + 75
Am I supposed to put the answer, too? It says "expression" so....
3. This one just has me completely lost. Do I divide or subtract or...? I have not the slightest idea what the answers are, how to set up the expression, how to make the table, etc. This is why I need help urgently, PLEASE. I'll try, though...
2,250 - 150 ÷ m
2,250 - 150 ÷ 6 =
2400 ÷ 6 = 400
2,250 - 150 ÷ 8
2400 ÷ 8 = 300
2,250 - 150 ÷ 10
2400 ÷ 10 = 240
Is this correct, or is it 2,250 ÷ 150 - m? I'm so lost. :/
1. Use n = 10 and n = 1 for both taxi services and compare.
2a. 35p + 105n
b. 2*65 + 37b + 75
3. Not dividing.
2250 - 150m = ?
Substitute minute values and solve.
1. To determine which service to choose for rides between 1 and 10 miles, let's compare the costs for each service.
For Supreme Taxi Service: Cost = 1.5 + 1.75n
For Town Taxi Service: Cost = 1.9 + 1.6n
Let's calculate the costs for different values of "n" within the range of 1 to 10 miles:
For 1 mile:
- Supreme Taxi Service: Cost = 1.5 + 1.75(1) = 3.25 dollars
- Town Taxi Service: Cost = 1.9 + 1.6(1) = 3.5 dollars
For 2 miles:
- Supreme Taxi Service: Cost = 1.5 + 1.75(2) = 4.25 dollars
- Town Taxi Service: Cost = 1.9 + 1.6(2) = 4.1 dollars
Continuing this calculation for different values of "n," we can find the costs for each service within the given range. By comparing the costs, we can determine which service to choose.
2. Let's write expressions for the number of calories in each situation:
a) "p" peaches and "n" bananas:
- The total calories for "p" peaches is: 35p
- The total calories for "n" bananas is: 105n
So, the expression for the number of calories in this situation would be: 35p + 105n.
b) Two slices of bread, "b" slices of bacon, and one egg:
- The total calories for two slices of bread is: 65 x 2 = 130
- The total calories for "b" slices of bacon is: 37b
- The total calories for one egg is: 75
So, the expression for the number of calories in this situation would be: 130 + 37b + 75.
3. The hot air balloon starts at a height of 2,250 feet and descends 150 feet each minute. To find its height after a certain number of minutes, we can subtract 150 times the number of minutes from the initial height.
Using this information, let's calculate the height of the balloon after six, eight, and ten minutes:
After six minutes:
Height = 2,250 - (150 x 6) = 2,250 - 900 = 1,350 feet
After eight minutes:
Height = 2,250 - (150 x 8) = 2,250 - 1,200 = 1,050 feet
After ten minutes:
Height = 2,250 - (150 x 10) = 2,250 - 1,500 = 750 feet
To write the expression for the balloon's height at "m" minutes, we can use the formula:
Height = 2,250 - (150 x m)