GRAPHING WITH RATIOS

Problem 1 :

• You are skateboarding at a pace of 30 meters every 5 seconds.
• Your friend is in-line skating at a pace of 9 meters every 2 seconds.

Graph each ratio relationship in the same coordinate plane. Who is faster?

Solution :

Distance covered = 30 meters 

Time taken = 5 seconds

Distance covered in 1 second = 30/5

= 6 meters

Let x be the time taken in seconds and y be the distance in meters.

y = 6x

The points are (1, 6) (2, 12) (3, 18) (4, 24) and (5, 30)

Distance covered = 9 meters 

Time taken = 2 seconds

Distance covered in 1 second = 9/2

= 4.5 meters

Let x be the time taken in seconds and y be the distance in meters.

y = 4.5x

The points are (1, 4.5) (2, 9) (3, 13.5) (4, 18) and (5, 22.5)

You are faster.

Problem 2 :

You buy 2.5 pounds of pumpkin seeds and 2.5 pounds of sunflower seeds. Use a graph to find your total cost. Then use the graph to determine how much more you pay for pumpkin seeds than for sunflower seeds.

Solution :

From the picture given picture above,

Cost of pumpkin seeds = $6.50 per pound

Let x be the number of pounds and y be the total cost.

y = 6.50x

The points are (1, 6.50) (2, 13) (3, 19.50) (4, 26) and (5, 32.5)

Cost of sunflower seeds = $4 per pound

Let x be the number of pounds and y be the total cost.

y = 4x

So, the points are (1, 4) (2, 8) (3, 12) (4, 16) and (5, 20)

From the graph,

• Cost of pumpkin seeds for 2.5 pounds = $16.25
• Cost of sunflower seeds for 2.5 pounds = $10

From the calculation,

Cost of pumpkin seeds for 2.5 pounds 

= 6.5(2.5) ==> $16.25

Cost of sunflower seeds for 2.5 pounds

= 4(2.5) ==> $10

Find the missing values in the ratio table. Then write the equivalent ratios.

Problem 3 :

Solution :

Chikens and eggs is in the ratio

= 8 : 6

Simplifying it, we get

= 4 : 3

Second column :

Let x be the unknwon.

x : 12 = 4 : 3

x/12 = 4/3

3x = 4(12)

x = 48/3

x = 16

Third column :

Let y be the unknown,

24 : y = 4 : 3

24/y = 4/3

3(24) = 4y

y = 3(24)/4

y = 3(6)

y = 18

Problem 4 :

Solution :

Fishes and snails is in the ratio

= 6 : 2

Simplifying it, we get

= 3 : 1

Second column :

Let y be the unknwon.

3 : y = 3 : 1

3/y = 3/1

3 = 3y

y = 1

Third column :

Let x be the unknown,

x : 4 = 3 : 1

x/4 = 3/1

x = 4(3)

x = 12

Fourth column :

Let y be the unknown,

15 : y = 3 : 1

15/y = 3/1

15 = 3y

y = 15/3

y = 5

Problem 5 :

Just by looking at the graph, determine who earns a greater hourly wage. Explain.

Solution :

Considering the blue line and red line, the slope of the blue line is greater then you earn more.

Problem 6 :

Your freezer produces 8 ice cubes every 2 hours. Your friend’s freezer produces 24 ice cubes every 5 hours. Graph each ratio relationship in the same coordinate plane. Whose freezer produces ice faster?

Solution :

Your freezer :

8 ice cubes for every 2 hours

In 1 hour, number of ice cubes produced = 8/2

= 4 ice cubes

Your friend's freezer :

24 ice cubes for every 5 hours

In 1 hour, number of ice cubes produced = 24/5

= 4.8 ice cubes

The blue line is more steeper than red line and comparing the calculation 4.8 is greater than 4.

Then, your friend's freezer produces faster.

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