Question

A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance traveled. Hopping Number of hops Distance traveled (ft)
20 30
50 75
80 120
120 ? Which statement correctly explains how to find the distance traveled after 120 hops? Subtract 120 – 75 to get 45, then add that number to 120. Add 30 + 75 + 120. 20 multiplied by 6 is 120, so you can multiply 30 times 6 to find the distance. 30 multiplied by 4 is 120, so you can multiply 20 times 4 to find the distance.

Answer 1

First we rewrite the table:

20    30

50    75

80    120

150   ?

We observe that for each 30 number of hops, the distance increases by 45 feet.

We must find the slope of the line:

m = (y2-y1) / (x2-x1)

m = (75-30) / (50-20)

m = 1.5

Then, the line is:

y = 1.5x

We substitute x = 150

y = 1.5 * (150)

y = 225

Answer:

Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.

Answer 2

Answer:

First we rewrite the table:

20    30

50    75

80    120

150   ?

We observe that for each 30 number of hops, the distance increases by 45 feet.

We must find the slope of the line:

m = (y2-y1) / (x2-x1)

m = (75-30) / (50-20)

m = 1.5

Then, the line is:

y = 1.5x

We substitute x = 150

y = 1.5 * (150)

y = 225

Answer:

Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.Step-by-step explanation: