Ratios

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#15469

Kim, Lou and Pat decided to sell hand-made necklaces at a local market. Kim invested $50, Lou $35 and Pat $40 to buy the beads. After two weeks they had sold $200 worth of necklaces. They decided to share this income in the same ratio as their original investment. Pat’s profit from the project was?

50:35:40
50 + 35 + 40 = 125 parts

200 ÷ 125 = $1.60

each part is worth $1.60

Pat contributed 40 parts
40 × 1.6

$64

[Admin]

#15470

In a particular state it was decided that post-primary schools and colleges with 360 students should have 30 teachers and that this ratio should be used for every school. The principal of a school wanted to find whether to 28 teachers was the correct number for 492 students or whether more teachers would be needed.
a. Calculate the preferred ratio of teachers to students.
b. How many more teachers are needed to meet this new ratio?
c. Another school has 288 students and 26 teachers. What staff changes would be needed to bring this school to the correct ratio?

a. 360:30
= 12:1

b. 492 ÷ 12 = 41, so would need an 41 – 28
= 13

c. 288 ÷ 12 = 24
need 24 teachers, so need to remove two teachers

 

[Admin]

#18864

Divide $1000 in the ratio 3:2.
1000 ÷ 5 = 200 ∴ each part is worth $200	there are 3 and 2 parts, which make 5 divide 1000 into 5 parts to find the value of each part
3 × 200 = $600 2 × 200 = $400 ∴ $600, $200	the first amount is 3 lots of $200 = $600 the second amount is 2 lots of $200 = $400

[Admin]

#18866

Three men invest money to buy a racehorse. Joe pays $7000. Tom pays $21 000 and Dave pays $49 000. After a year, the horse has won the total prize money of $1.1 million. If the prize money is divided in the same ratio as the men invested, how much does Tom receive?
1.1 million = 1,100,000	convert the 1.1 million into a number by multiplying 1.1 by 1 000 000
Total = 7 000 + 21 000 + 49 000 = 77 000	find the total of the investments
1 100 000 ÷ 77 000 = $14.29	split the prize money into 77,000 parts to find out what each share or part is worth so each part is worth $14.29
210 00 × $14.29 = $300 090	Tom put in $21,000 so he will get 21 000 lots of $14.29

[Admin]

#18868

The human body is made up of water, protein and bone in the ratio 7:2:1 respectively. Mary’s body contains 42kg of water. What is her total weight?
42 ÷ 7 = 6 so each part = 6 kg	Water represents 7 parts of the ratio. to find how much each part is we divide 42 by
protein = 2 × 6 = 12kg	there are 2 parts of protein, so multiply 6 by 2
bone = 1 × 6 = 6 kg	there are 1 parts of bone, so multiply 6 by 1
total mass = 42 + 12 + 6 = 60 kg	find the total weight by adding water, protein and bone

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