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aksik [14]
1 year ago
9

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

punds he lost the first week. The third week, he lost 1 more pound than 3/4 of the pounds he lost the first week.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. The second week, he lost 4 pounds less than 5/2 times the pounds luke lost the first week. The third week, he lost 1/2 more than 5/4 times the pounds luke lost the first week. Assuming they both lost the same number of pounds over the three weeks, complete the following sentences1. The expression for luke's weight loos over the three weeks is ______2. The expression for liam's weight loss over the three weeks is ______3. The number of pounds luke lost in the fist week is ____4. The number of pounds luke and liam each lost over the three weeks is ____And the answer bank has2 pounds13/4x-1/28/4x-9/221/4x-9/24 pounds 6 pounds
Mathematics
1 answer:
irga5000 [103]1 year ago
7 0

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

=========================================================

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

=============================================================

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

=============================================================

4. The number of pounds luke and liam each lost over the three weeks is

= 13/4 * 2 - 1/2 = 6 pounds

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