4.06 Applications of Ratios

Find the total number of parts in the following ratios.

Divide each of the following amounts in the given ratio.

Divide \$500 into the following ratios:

Helen and Sam scored a total of 45 goals in their netball game in the ratio 4:5.

\$25 is shared between Valentine and Neil in the ratio 7:3.

Divide 32 kilometres in the ratio of 6:2.

Amelia and Christa agree to divide \$1000 in the ratio 13:7.

James and Ray share \$40 in the ratio 1:4.

The ratio of males to females on a train is 8:3. If the train is carrying 264 passengers:

Divide 30 kilometres in the ratio 4:7:4.

90 is divided into three parts A, B, and C in the ratio 3:2:1.

162 is divided into three parts A, B, and C in the ratio 9:5:4.

A line of length 144\text{ cm} is divided into three segments A, B, and C in the ratio 7:5:6. Find the length of:

The angles in a triangle are in the ratio 1:4:7. Find the measure of:

The length of a garden bed is split into three sections for carrots, potatoes and parsley respectively in the ratio 3:1:4. If the total length is 16\text{ m}, find the length of the side for:

Concrete is mixed in the ratio of 1 part cement, 2 parts sand and 3 parts gravel. How much cement is needed for 9.6 cubic metres of concrete?

The gas in a container consists of 7 parts oxygen and 6 parts helium. How many litres of oxygen are present if there are 520 litres of gas in the container?

The numbers of red, blue, green and white jelly beans in a lolly bag are found to be in the ratio of 3:3:5:2. If there are 78 jelly beans in the bag, how many blue jelly beans are there?

56\text{ kg} of a metal alloy is made up of tin and zinc in the ratio 3:5.

A journalist spent a total of 54 hours researching, writing and editing a news report. She spent 27 hours researching and 12 hours writing.

Sally and Mae want to share 1000 \text{ g} of sugar in the ratio 21:29. How much sugar will:

When buying a \$10 scratch ticket, Buzz paid \$6 and Neil paid \$4. If they share the \$40\,000 winnings in the same ratio as they contributed, how much will:

Ada, Simone and Lilian invest \$3000, \$5000, and \$7000 respectively into a new business. In the first year, they make a profit of \$60\,000 which they share in the same ratio as their investment. How much should each person receive?

The perimeter of a rectangle is 90\text{ cm} and the ratio of its length to its width is 6:3.

The perimeter of a rectangle is 198 and the ratio of length to width is 6:5.

Idat wants to estimate the total population of skinks in his backyard. He performs a capture-recapture, marking 12 individuals in the first capture and finding 3 marked out of the 9 individuals in the second capture. Determine the total population of skinks.

Henry wants to estimate the total population of fish in his pond. He performs a capture-recapture, marking 8 individuals in the first capture and finding 6 marked out of the 11 individuals in the second capture. Determine the total population of fish to the nearest whole number.

Angela wants to estimate the total population of wild geese in her local park. She performs a capture-recapture, marking 9 individuals in the first capture and finding 2 marked out of the 10 individuals in the second capture. Determine the total population of geese.

A local council wanted to monitor the number of rabbits in the area. They used the capture-recapture technique to estimate the population of rabbits. 161 rabbits were caught, tagged and released. Later, 32 rabbits were caught at random. 7 of these 32 rabbits had been tagged.

The capture-recapture technique was used to estimate the population of cuttlefish. At the beginning of the year the number of cuttlefish caught, tagged and released was 300. When 250 cuttlefish were taken at the end of the year, 50 of them were found to be recaptured tagged ones.