Luke started a weight-loss program.
The first week, he lost X pounds.
the second week he lost 3/2 pounds less then 3/2 times the pounds he lost the first week. so, he lost 3/2 x - 3/2
The third week, he lost 1 more pound than 3/4 of the pounds he lost the first week. so, he lost 3/4 x + 1
So, over 3 weeks he lost :
x + (3/2 x - 3/2) + (3/4 x + 1) = 13/4 x - 1/2
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Liam started the program when Luke did.
The first week, he lost 1 pound less than 3/2 times the pounds luke lost the first week. so, he lost (3/2 x - 1)
The second week, he lost 4 pounds less than 5/2 times the pounds luke lost the first week. so ,he lost (5/2 x - 4)
The third week, he lost 1/2 more than 5/4 times the pounds luke lost the first week. so, he lost, ( 5/4 x + 1/2)
The expression for Liam's weight loss over the three weeks is =
= (3/2 x - 1) + (5/2 x - 4) + ( 5/4 x + 1/2) = 21/4 x - 9/2
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Assuming they both lost the same number of pounds over the three weeks
So, equating the number of pounds lost by each one of them
so,
13/4 x - 1/2 = 21/4 x - 9/2
solve for x
13/4 x - 21/4 x = -9/2 + 1/2
-2x = -4
divide both sides by -2
so,
x = -4/-2 = 2
so,
The number of pounds luke lost in the fist week is 2 pounds
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4. The number of pounds luke and liam each lost over the three weeks is
= 13/4 * 2 - 1/2 = 6 pounds