General exam questions

Example 1

A baby’s weight increases by 7% over a month from birth to 3.9kg. What was the baby’s weight at birth?

NOTE:

A 7% increase on 100% is 107%

Multiply both sides by 3.9 to get x on its own (remember - what you do to one side you do to the other).

(100times3.9)/107=(xtimescancel3.9)/cancel3.9

(100times3.9)/107=x

x=(100times3.9)/107

x=3.64

Answer: The baby’s weight at birth was 3.64kg

Example 2

John buys a drill for £150.00 inc sales tax and James buys the same drill using a trade account for £120.00 exc sales tax. If sales tax is charged at 20% how much tax did John and James pay and who paid the least in total for the drill?

First work out what James paid.

Multiply both sides by x to get x on its own

(100timesx)/20=(120timescancelx)/cancelx

(100x)/20=120

Multiply both sides by 20 to get x on its own

(100xtimescancel20)/cancel20=120times20

100x=120times20

Divide both sides by 100 to get x on its own

(cancel100x)/cancel100=(120times20)/100

x=(120times20)/100

x=(24cancel00)/(1cancel00)

x=24

James paid £24.00 tax on his drill and a total of £120.00 + £24.00 = £144.00

Now lets work out what John paid.

NOTE:

£150.00 is including the 20% sales tax so is equal to 120%?

Multiply both sides by 150.00 to get x on its own

(100times150)/120=(xtimescancel150)/cancel150

(100times150)/120=x

x=(100times150)/120

x=125

John paid £125.00 excluding sales tax for his drill, so the sales tax he paid was:

£150.00 - £125.00 = £25.00

Answer: John paid £25.00 sales tax on his drill and £150.00 in total

James paid £24.00 in sales tax on his drill and £144.00 in total

So James paid less for his drill.