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Question 73653This question is from textbook Prentice Hall Mathematics Pre-Algebra
: Hi guys, I am not doing well with helping my son on these word problems. Will you please assist me with the four question I have submitted below. Thanks!
Hello, I have a few word problem questions. Please help with...
This is question # 32 on page 17 of the text book.
1. A carnival charges $5 for admission plus $2 per ride.
a. Write an expression for the cost of admission plus r rides.
b. Find the cost of admission plus six rides.
c. How many rides can you afford if you have $15 to spend?
This is question # 16 on page 16 of the text book.
2. Online Purchasing - An online video store charges $24 for each DVD. Shipping costs $4 per order.
a. Write a variable expression for the cost of ordering DVDs.
b. Find the cost of ordering 3 DVDs.
This is question # 27 on page 16 of same text book.
3. Marine Biology - Write an expression for the number of kilometers a dolphin travels in d hours swimming at 8 km/h. Then find the number of kilometers the dolphin travels in 3 hours.
Finally, this is question # 31
4. A fitness club requires a $100 initiation fee and dues of $25 each month. Write an expression for the cost of membership for n months. Then find the cost of membership for one year.
This question is from textbook Prentice Hall Mathematics Pre-Algebra
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Page 17...#32
A carnival charges $5 for admission plus $2 per ride.
a. Write an expression for the cost of admission plus r rides.
The cost of admission is fixed at $5.
The cost of rides is a variable and depends on the number of rides and here, this is called r. So you can write: The total cost is fixed cost ($5) plus $2 times the number of rides ($2(r))
The cost of r rides is: $5+$2(r)
b. Find the cost of admission plus 6 rides.
Here, the variable r (number of rides) now has a value of 6, so you can substitute this value (6) in place of r in the expression in part a. This will then give you the total cost, which you can call C.
From a. you have:
C = $5+$2(r), but r = 6, so...
C = $5+$2(6) Multiply the $2 times 6 = $12
C = $5+$12 Add these.
C = $17 This is the cost of admission plus 6 rides.
c. How many rides can you afford if you have $15 to spend?
Well, first, you know that you will have to spend $5 of your $15 just to get into the carnival. That's the admission charge. So now you have $10 ($15-$5 = $10) left for rides. How many rides can you get for $10? Let's use the equation for the total cost, C, we wrote in part b to find out:
(C = $5+$2(r)) Since you have a total of $15 to spend, the total cost, C, is going to be $15, so you can set C = $15
$15 = $5+$2(r) Now you do some algebra. Subtract $5 from both sides of this equation.
$15-$5 = $5-$5+$2(r) Simplify this.
$10 = $2(r) Now you want to get r by itself so you will divide both sides by $2.
$10/$2 = $2(r)/$2 Simplify this.
5 = r
Answer: You can get 5 rides if you have $15 to spend.
Check:
C = $5+$2(r) Substitute r = 5.
C = $5+$2(5) Simplify.
C = $5+$10
C = $15 This is the total cost for 5 rides.
I have to take a short break, but I shall return!
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I'm back.
Page 16....#16
Here we have a fixed cost of $4 for shipping and a variable cost for the DVDs of $24 per DVD. The variable cost will depend, of course, on the number of DVDs ordered, so you will want to give this variable a "name". Let's call it D (For DVD). Now you can write a variable expression for the for the cost of ordering DVDs.
$4+D($24) This is the variable expression.
The cost for ordering 3 DVDs can be found by letting the variable, D, = 3.
Let's call the total cost, C, so you can write...
C = $4+D($24) But D = 3 so substitute 3 for D in this equation.
C = $4+3($24) Multiply the 3 times $24 = $72.
C = $4+$72
C = $76 This is the total cost of ordering 3 DVDs.
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Page 16...#27
For each hour the dolphin travels, it covers s distance of 8km. (8km/hr)
If the dolphin travels for h hours, then the distance covered can be expressed by:
(h)hrs*(8km/hr)
Now if the dolphin travels for 3 hours, then you can set h = 3 and substitute this for h in the above expression.
3hrs(8km/hr)= 24km
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Page 17...#32
Here, we have a fixed cost of $100 (initiation fee) and a variable cost of $25 per month. If n = the number of months, then you can express the cost of membership for n months as: Fixed cost plus variable cost, or...
$100+n($25)
To find the cost of membership for 1 year, you first must convert 1 year into 12 months. Why, because the variable (n) in the above expression stands for the number of months, not years. So, let n = 12 (months) and substitute 12 for n in the expression. The cost of membership for 1 year (12 months) is:
$100+12($25)= $100 + $300 = $400
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