The height of Luke is 23 of the height of Raj. The ratio of the height of Raj to that of Emma is 4 : 5. Find the ratio of the height of Emma to the total height of Raj and Luke.(1) 3 : 4(2) 4 : 3 (3) 4 : 15(4) 15 : 4
Question
The height of Luke is 23 of the height of Raj. The ratio of the height of Raj to that of Emma is 4 : 5. Find the ratio of the height of Emma to the total height of Raj and Luke.(1) 3 : 4(2) 4 : 3 (3) 4 : 15(4) 15 : 4
Solution
Step 1: Let's denote the height of Raj as R, the height of Luke as L, and the height of Emma as E.
Step 2: From the problem, we know that L = 2/3 R and the ratio of R to E is 4:5. This means that R = 4/5 E.
Step 3: We can substitute the value of R from step 2 into the equation from step 1 to find the height of Luke in terms of E. This gives us L = 2/3 * 4/5 E = 8/15 E.
Step 4: The total height of Raj and Luke is R + L = 4/5 E + 8/15 E = 52/75 E.
Step 5: The ratio of the height of Emma to the total height of Raj and Luke is E : (R + L) = E : 52/75 E = 75 : 52.
However, this ratio is not listed in the options. There might be a mistake in the problem or the options.
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