USING RATIOS WORKSHEET

Problem 1 :

Sheldon and Leonard are partners in a business. Sheldon makes $2 in profits for every $5 that Leonard makes. If together they make a profit of $28 on the first item they sell, how much profit does Sheldon make ?

Solution :

Step 1 :

Given : Sheldon’s profit is $2 and Leonard's profit is $5.

Total profit = 2 + 5 = $7.

The ratio of Sheldon’s profit to the total profit is

$2/$7

Let S be the Sheldon's profit for the given total profit $28.

Then, we have

Step 2 :

Let us use ratio reasoning to find S.

Because $7 x 4 = $28, multiply $2 by 4.

Therefore, if they make a total profit of $28, then Sheldon makes a profit of $8.

Problem 2 :

The members of the PTA are ordering pizza for a meeting. They plan to order 2 cheese pizzas for every 3 pepperoni pizzas they order. How many cheese pizzas will they order if they order a total of 25 pizzas ?

Solution :

Step 1 :

Given : 2 cheese pizzas for every 3 pepperoni pizzas.

Total profit = 2 + 3 = 5 pizzas

The ratio of cheese pizzas to total pizzas is

2/5

Let C be the number of cheese pizzas for the given total pizzas 25.

Then, we have

Step 2 :

Let us use ratio reasoning to find C.

Because 5 × 5 = 25, multiply 2 by 5.

Therefore, if they order a total of 25 pizzas, then they will order 10 cheese pizzas.

Problem 3 :

Two pizzas cost £17.00. Calculate the cost of five pizzas

Solution :

Cost of 2 pizzas = £17

Let x be the cost of five pizzas

Ratio between number of pizzas and cost.

2 : 17 = 5 : x

2/17 = 5/x

2x = 5(17)

x = 5(17)/2

x = 42.5

So, cost of 5 pizzas is $42.5

Problem 4 :

Peanuts cost 60p for 100 grams, what is the cost of 350 grams of peanuts?

Solution :

Cost of 100 grams of peanuts = 60p

Ratio between quantity of peanuts to price 

= 100 : 0.60

Let the cost of 350 grams of peanuts be x.

100 : 0.60 = 350 : x

100/0.60 = 350/x

100x = 350(0.60)

x = 350(0.60)/100

x = 2.1

Cost of 350 grams of peanuts is 2.1

Problem 5 :

A stephenson monument is a large statue in Newcastle it is 30 m wide and 74 meters tall.

She makes a scale model of Stepenson mounument her model is 37 centimeters tall. How wide is her model ?

Solution :

Ratio between width and height of Statue is 30 : 74

Let x be the new width of the model.

Height of the model = 37 cm

30 : 74 = x : 37

30/74 = x/37

x = 30(37)/74

x = 30/2

x = 15

So, the width of the mode is 15 cm.

Problem 6 :

Purple paint is made by mixing blue and red paint

Use the picture to work out the missing numbers. For 25 tins of purple paint you need ____ tins of blue paint and ___ tins of red paint ?

Solution :

Ratio between blue to red paint to make purple paint is 

3 : 2 : 5

To make 5 as 25, we have to multiply the entire ratio by 5

3(5) : 2(5) : 5(5)

15 : 10 : 25

Number of tins of blue paint = 15

Number of tins of red paint = 10

Problem 7 :

The map has a scale of 1 centimeters to 6 km

The road from Ridlington to Carboard measured on a map is 6.6 cm long. What is the length of road in kilometers ?

Solution :

Ratio between distance in scale to original distance

= 1 : 6

When the distance in scale is 6.6 cm, let x be the original distance.

1 : 6 = 6.6 : x

1/6 = 6.6/x

x = 6.6(6)

x = 39.6

So, the original distance is 39.6 km.

Problem 8 :

A fish swam a distance of 5,104 yards. How far did the fish swim, in miles? (1 mile = 1,760 yards)

A) 0.3    B) 2.9    C) 3,344      D) 6,864

Solution :

1 mile = 1760 yards

Ratio between miles to yards = 1 : 1760

Let x the required distance in miles

1 : 1760 = x : 5104

1/1760 = x/5104

x = 5104/1760

x = 2.92

So, option B is correct.

Problem 9 :

Nasir bought 9 storage bins that were each the same price. He used a coupon for $63 off the entire purchase. The cost for the entire purchase after using the coupon was $27. What was the original price, in dollars, for 1 storage bin?

Solution :

Number of storage bins purchased = 9

Amount of coupon = $63

Amount spent after using coupon = $27

Total cost = 63+27

= 90

Cost of 9 storage bins = 90

Cost of 1 storage bin = 90/9

= $10.

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