math help. Algebra

Question

1. An architect built a scale model of a shopping mall. On the model, a circular fountain is 15 inches tall and 7.5 inches in diameter. If the actual fountain is to be 10 feet tall, what is its diameter?

 

2.  Hidemi is a waiter. He waits on a table of 4 whose bill comes to $90.27. If Hidemi receives a 15% tip, approximately how much will he receive? 

 

3.  Salar's Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $3.50 each and he has $15.25 to spend, how many tickets can he buy? 

 

4. A man that is 6 feet tall casts a shadow 5 feet long. At the same time, a lamppost beside the man casts a shadow 25 feet long. How tall is the lamppost? 

 

 

5. The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 4:12. There are 24 gallons of gasoline. How many ounces of oil are there? 

Answer 1

Hi Lindsey,

 

A nice passel of problems here !!

 

We'll consider each one in turn.

 

 

Problem #1 (fountain diameter):

 

We'll use the concept of proportion (equivalent ratios) to set up this proportion to solve for our unknown (x):

 

    scale height : actual height = 

    scale diameter : actual diameter

 

    15 inches : 120 inches = 7.5 inches : x inches

    1.25 feet : 10 feet = 0.625 feet : x feet

    1.25/10 = 0.625/x

    (1.25)(x) = (10)(0.625)

    1.25x = 6.25

    x = 6.25/1.25

    x = 5 feet (fountain diameter)

 

We can verify our answer by plugging it back into our proportion and see if the ratios are equal:

    1.25/10 = 0.625/5

    1/8 = 1/8 (ratios are equal)

 

Since our proportion with our plugged-in answer yields equal ratios, we are confident that our answer is correct.

 

 

Problem #2 (tip received):

 

We can use this equation expressing the tip received (x) as the bill amount times the given percentage:

    15% = 15/100 = 0.15

    x = (90.27)(0.15)

    x = 13.5405

    x = $13.54 (tip received to nearest penny)

 

 

Problem #3 (number of tickets):

 

We can use this equation expressing the number of tickets (x) as the spending allowance divided by the unit price of a ticket:

    x = 15.25/3.50

    x = 61/14

    x = 4 and 5/14

    x = 4 tickets (disregarding remainder fraction)

 

 

Problem #4 (height of lamp post):

 

This problem is similar to our approach used to solve Problem #1 (fountain diameter).  We can use this proportion to solve for our unknown (x):

 

    height of man : shadow of man =

    height of lamp post : shadow of lamp post

 

    6 feet : 5 feet = x feet : 25 feet

    6/5 = x/25

    (6)(25) = (5)(x)

    5x = 150

    x = 150/5

    x = 30 feet (height of lamp post)

 

We can verify our answer by plugging it back into our proportion and see if the ratios are equal:
    6/5 = 30/25

    6/5 = 6/5 (ratios are equal)

Since our proportion with our plugged-in answer yields equal ratios, we are confident that our answer is correct.

 

 

Problem #5 (ounces of oil):

Again, this problem is similar to our approach used to solve Problem #1 (fountain diameter). We can use this proportion to solve for our unknown (x):

    ounces of oil : gallons of gasoline =
    ounces of oil : gallons of gasoline

 

    4 ounces : 12 gallons = x ounces : 24 gallons
    4/12 = x/24
    (4)(24) = (12)(x)
    12x = 96

    x = 96/12

    x = 8 ounces of oil

We can verify our answer by plugging it back into our proportion and see if the ratios are equal:
    4/12 = 8/24
    1/3 = 1/3 (ratios are equal)

Since our proportion with our plugged-in answer yields equal ratios, we are confident that our answer is correct.

 

 

The majority of these problems demonstrated the powerful concept of proportion (equivalent ratios) in solving problems when three of the values are known and we need to determine the unknown fourth value.

 

Thanks for submitting these problems & glad to help.

 

God bless, Jordan.