Respuesta :
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
How to calculate the value?
Luke's weight loss journey;
Weight luke lost in the first week; x pounds
The 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
The 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 the 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, the total weight lost by Luke and Liam each = ¹³/₄(2) - ¹/₂ = 6 pounds
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Luke started a weight-loss program. The first week, he lost x pounds. The second week, he lost pounds less than times the pounds he lost the first week. The third week, he lost 1 pound more than of the pounds he lost the first week.
Liam started a weight-loss program when Luke did. The first week, he lost 1 pound less than times the pounds Luke lost the first week. The second week, he lost 4 pounds less than times the pounds Luke lost the first week. The third week, he lost pound more than times the pounds Luke lost the first week.
Assuming they both lost the same number of pounds over the three weeks, complete the following sentences.
[tiles inserted here]
9/4x - 9/2
21/4x - 9/2
6 pounds
4 pounds
13/4x - 1/2
2 pounds
The expression for Luke's weight loss over the 3 weeks is [ blank here ]
The expression for Liam's weight loss over the 3 weeks is [ blank here ]
The number of pounds Luke lost in the first week is [ blank here ]
The number of pounds Luke and Liam each lost over the three weeks is [ blank here ]
