Mathex questions help please! ?

Question

Thanks so much, please tell me how you worked it out in simple explanations please if you can!! lurve youu!! :]

1. In the old units a hundredweight was actually 112 pounds. A kilogram is 2 and a quarter pounds. How many kilograms is in a hundredweight to the nearest kilogram?

2. Billy and Bob went shopping. Billy started with $15 more than Bob. Billy spent twice as much as Bob. when Billy finished shopping he only had half as much money as he had started with. If Bob finished with $6, how much did he start with?

3. A contract worker pays 12.5% gst on her earnings. Last week she paid $100 gst. what did she earn that week?

thank you everyone!

Answer 1

Just divide 112 lb by 2.25 lb/kg:

112 lb / (2.25 lb/kg) ≈ 49.8 kg ≈ 50 kg to the nearest kilogram.

Remember, when we divide using units in a fractions, we treat the units like fractions as well, and invert them also, just as we do the numerical values.  

2.  Let x be the amount Bob started with.  Then Billy started with x + $15.  Let the amount Bob spent be y.  Then Billy spent 2y.  Now we can set up these equations:

x - y = $6 ----> y = x - $6

x + $15 - 2y = (x + $15)/2

2x + $30 - 4y = x + $15  (We multiplied through by 2)

x + $15 - 4y = 0

x + $15 = 4y

Now plug in (x - $6) for y above:

x + $15 = 4 (x - $6)

x + $15 = 4x - $24

$39 = 3x

$13 = x

Now let's verify this is correct.  If Bob was left with $6, then he spent $7: $13 - $6 = $7.  That means that Billy spent 2 ($7) = $14.  Also, if Billy started with $15 more than Bob, he had $13 + $15 = $28 to start with.  We also note that $28 - $14 = $14, which is half of Billy's original starting amount, as stipulated in the problem. Therefore, the calculated answer appears to be correct.  Bob started with $13.

3.  What this means is that $100 was 12.5 % of the worker's earnings.  So to find her earnings, we can set up this equivalence ratio:

12.5/100 = $100/x.  Then solve for x:

12.5x = $10,000

x = $10,000/12.5

x = $800.

The worker's earnings for the week were $800.