Algebra-RatioProportionWork

Question 1

At a time of day when a 12 foot flagpole casts a 7 foot shadow, how long is the shadow of a 5 foot person?

Answer 1

The ratio (height of object)/(length of shadow) is constant:

(height_of_object)/(length_of_shadow)=12/7.

5/x = 12/7
=> x = 35/12

Question 2

How do you write the fraction 12/5 in Latex?

Answer 2

$ \frac{35}{12} $

Question 3

Lee can make 18 cookies with two cups of flour. How many cookies can he make with three cups of flour?

Answer 3

(18 cookies)/(2 cups_of_flour) =(x cookies)/(3_cups_of_flour)
=> x = 27

Question 4

Amount of butter, number of cookies you can bake. DP or IP?

Answer 4

DP

Question 5

Speed you drive, time to get to destination

Answer 5

IP

Question 6

Base of a triangle, area of a triangle (assume the height stays the same)

Answer 6

DP

Question 7

Side length of a square, area of a square

Answer 7

Neither! Although doubling the side length does increase the area, it doesn’t double it - it quadruples it! To get DP, you actually need the ratio of these ideas to be CONSTANT. Here, it is (s^2)/s=s, which isn’t a constant. Be careful.

Question 8

A rectangle is formed by increasing one pair of sides of a square by 25 percent. By what percent must the other two sides be decreased to form a new rectangle with the same area as the original square?

Answer 8

The product LW is constant. => L and W are in inverse proportion.

In a square, L_square = W_square.

To increase by 25% means to take the original length s and to add 25% of s.

s+(25/100)⋅s=s+(1/4)⋅s=(5/4)⋅s

  ==>  L_rect=(5/4)⋅s
L_square * W_square = L_rect * W_rect
==> s⋅s = L_rect  ⋅ W_rect
==> s⋅s =  (5/4)⋅s⋅ W_rect
==> W_rect = (4/5)⋅s

==> We start with s (or 1⋅s), and we end with 0.8s. Thus, the change is 0.2s=20% of the original width.

Question 9

Two quantities are in direct proportion if ….

Answer 9

Two quantities are in direct proportion if their ratio remains constant.

Question 10

Two quantities are in inverse proportion if …

Answer 10

Two quantities are in inverse proportion if their product remains constant.

Question 11

What is the fundamental equation relating rate, time and distance?

Answer 11

d=rt

Question 12

if the rate is held constant, what do we know about time and distance?

Answer 12

If the rate is a constant, then we have d/t=constant. Direct Proportion.

Question 13

if the distance is constant, then what’s the relationship between rate and time?

Answer 13

IP. If distance is constant, then rt = constant. So rate and time are inversely proportional.

Question 14

If we double the rate of speed, keep distance constant, what happens to time?

Answer 14

if we double our rate of speed, then we can cover the same distance in half the time.

Question 15

If I drive to work at 50 miles per hour, it takes me 40 minutes to get to work. How long will it take me to get to work if I drive at 60 miles per hour?

Answer 15

40*50=60t
40*5=6t
20*5=3t
100=3t
33 1/3