A reliable method
Introduce one scale factor for all ratio parts. For mixtures, conserve the amount of the active ingredient. For ages, add the same elapsed time to both people.
The common trap
An equal addition to two quantities does not preserve their ratio. A concentration average is weighted by volume rather than by the number of containers.
Check the conclusion
Check both the starting and ending relationships. A valid mixture should fall between the source concentrations when both contributions are positive.
Contrast the cases
A ratio 2:3:5 has ten total parts, so the second partner receives three tenths of the total. For accounts in ratio 3:2, write 3t and 2t. If six accounts are added only to the second category and the ratio becomes 3:4, the equation 3t/(2t+6)=3/4 gives t=3 and first count 9. In a mixture, the conserved quantity is active ingredient, not the ratio label.
Transfer and explain
Transfer: mix 20% and 40% solutions to make 10 liters at 28%. Let x denote the 20% portion: 0.2x+0.4(10−x)=2.8, giving x=6. Check that the 40% portion is 4 liters and both totals agree.
Three partners divide $210 in the ratio 2:3:5. How many dollars does the second partner receive?
- The total number of ratio parts is 10.
- The second partner receives 3 of those 10 parts.
- The amount is 210 × 3/10 = 63.
Compare the other answer choices
Returns one ratio unit.
Divides equally despite unequal ratio parts.
Uses the other partners as denominator rather than the total.
Uses the third partner’s share.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
GMAT exam contentSiyavula Grade 10 mathematics foundation reference