A) The expression for Luke's weight loss over the 3 weeks is;
¹³/₄x - ¹/₂ pounds
B) The expression for Liam's weight loss over the 3 weeks is;
²¹/₄x - ⁹/₂ pounds
C) The number of pounds Luke lost in the first week is;
x = 2 pounds
D) The number of pounds Luke and Liam each lost over the three weeks is;
6 pounds
- Luke's weight loss journey;
Weight luke lost in the first week; x pounds
Weight he lost in the second week is 3/2 pounds less than 3/2 times the pounds he lost in the first week. Thus;
Weight luke lost in the second week = ³/₂x - ³/₂ pounds
In the third week, he lost 1 pound more than 3/4 of the pound he lost in the first week. Thus;
Weight luke lost in the third week = (³/₄x) + 1 pounds
Total weight lost by luke in 3 weeks = x + ³/₂x - ³/₂ + ³/₄x + 1
⇒ ¹³/₄x - ¹/₂
- Liam's weight loss journey;
First week he lost 1 pound less than 3/2 times the pounds luke lost in the first week
Weight Liam lost in the first week; ³/₂x - 1 pounds
Weight he lost in the second week is 4 pounds less than 5/2 times the pounds luke lost in the first week. Thus;
Weight Liam lost in the second week = ⁵/₂x - 4 pounds
In the third week, he lost 1/2 pound more than 5/4 of the pound luke lost in the first week. Thus;
Weight Liam lost in the third week = (⁵/₄x) + ¹/₂ pounds
Total weight lost by Liam in 3 weeks = ³/₂x - 1 + ⁵/₂x - 4 + ⁵/₄x + ¹/₂
⇒ ²¹/₄x - ⁹/₂ pounds
We are told that Luke and Liam lost same weight over 3 weeks. Thus;
¹³/₄x - ¹/₂ = ²¹/₄x - ⁹/₂
⇒ ²¹/₄x - ¹³/₄x = ⁹/₂ - ¹/₂
⇒ 2x = 4
x = 4/2
x = 2
Thus, total weight lost by Luke and Liam each = ¹³/₄(2) - ¹/₂ = 6 pounds
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