If X gets 25% more than Y, and Y gets 20% more than Z, what is the ratio of shares of X, Y,...
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If X gets 25% more than Y, and Y gets 20% more than Z, what is the ratio of shares of X, Y, and Z?
Show answer & explanation
The problem involves sequential percentage increases. By expressing X and Y in terms of Z and simplifying the resulting ratio to the smallest whole numbers, we find the ratio to be 15:12:10.
Step-by-step Derivation:
Step 1: Let the share of Z be $z$.
Step 2: According to the problem, Y gets 20% more than Z. Therefore, $Y = z + 0.20z = 1.2z$.
Step 3: X gets 25% more than Y. Therefore, $X = 1.2z + 0.25(1.2z) = 1.2z imes 1.25 = 1.5z$.
Step 4: Write the ratio of X : Y : Z as $1.5z : 1.2z : 1z$.
Step 5: Simplify the ratio by dividing by $z$: $1.5 : 1.2 : 1$.
Step 6: To convert these decimals into whole numbers, multiply all terms by 10: $15 : 12 : 10$.
Step 7: Check for common factors: 15, 12, and 10 have no common divisor other than 1, so the ratio is in its simplest form.