Ratio Problems

The blue parts already agree.

Match the B parts.

Use a common multiple for the Q parts.

Match B, then select only A and C.

Notice that blue is first in both given ratios.

For every 3 blue beads, how many red beads are there?

Part (a)

1. Red : blue =2:3=8:12.
2. Blue : yellow =4:5=12:15.
3. The ratio is 8:12:15.

Part (b)

1. The simplified ratio gives b=12.

Part (c)

1. The simplified ratio gives c=15.

Use the same number of raisin parts.

Part (a)

1. Oats : raisins =9:12. Raisins : seeds =12:10.
2. The combined ratio is 9:12:10.

Part (b)

1. The simplified ratio gives b=12.

Part (c)

1. The simplified ratio gives c=10.

Use 6 A parts to link the statements.

1. A:B=6:10.
2. When A has 6 parts, C has 7, so B:C=10:7 and x=7.

Calculate each income before forming the ratio.

Part (a)

1. Morning: 24\times3=72 pounds. Afternoon: 18\times4=72 pounds.
2. 72:72:36=2:2:1.

Part (b)

1. The simplified ratio gives b=2.

Part (c)

1. The simplified ratio gives c=1.

Combine the ratios before finding the whole.

1. Red : blue : green =6:4:5.
2. Total parts: 6+4+5=15. Blue fraction: \frac4{15}.

Make the number of orange parts the same in both ratios, then use the total.

1. Red : orange =2:3=4:6, and orange : yellow =6:5.
2. So red : orange : yellow =4:6:5, which is 4+6+5=15 parts.
3. One part: 180\div15=12 sweets.
4. Orange: 6\times12=72 sweets.

You can find blue first, then green.

1. Blue: 45\div3\times4=60.
2. Green: 60\div5\times6=72.

Compare the concentrate amounts for the same water amount.

1. A concentrate: 77\div7\times2=22 litres.
2. B concentrate: 77\div11\times3=21 litres.
3. Difference: 22-21=1 litre.

Find actual colour counts before combining the bags.

Part (a)

1. Bag A: 40\div5=8, so 16 red and 24 blue. Bag B: 30\div5=6, so 6 red and 24 blue.
2. Altogether: 22 red and 48 blue, so 22:48=11:24.

Part (b)

1. The simplified ratio gives b=24.

Change the number of blue beads, not every ratio term.

Part (a)

1. Original counts:20 red,30 blue,50 green.
2. New counts:20 red,20 blue,50 green.
3. 20:20:50=2:2:5.

Part (b)

1. The simplified ratio gives b=2.

Part (c)

1. The simplified ratio gives c=5.

Write red : blue : green as one ratio. How many more parts does green have than red?

1. Red : blue =4:3=8:6 and blue : green =2:5=6:15, so red : blue : green =8:6:15.
2. Green has 15-8=7 more parts than red.
3. 5 parts each: 7\times5=35 more green counters, which is fewer than 40. 6 parts each: 7\times6=42, which is at least 40.
4. So the least is 6 counters per part. Total parts: 8+6+15=29.
5. Least possible total: 29\times6=174 counters.

Compare the ratios using the unchanged number of blue counters.

1. Original red : blue =12:20. New red : blue =15:20.
2. The extra 3 parts are 12 counters, so one part is 4 counters.
3. Original red: 12\times4=48.

Find the original counts and update the total after removal.

1. Combined ratio: 6:10:15, totalling 31 parts.
2. There are 60 red,100 blue and 150 green counters.
3. 50 green counters leave, so 310-50=260 remain.
4. Blue fraction: 100/260=5/13.

Use the difference between A and C in the combined ratio.

1. A:B:C=12:21:14.
2. The difference is 2 parts, so one part is 10\div2=5.
3. B=21\times5=105.

Work with actual concentrate and water volumes.

1. A contains 150 ml concentrate and 450 ml water.
2. B contains 200 ml concentrate and 300 ml water.
3. Combined: 350 ml of concentrate and 750 ml of water.
4. For 1:3, water must be 350\times3=1050 ml.
5. Add 1050-750=300 ml of water.