Question

Jimmy has 28% more pens than Kate. If Jimmy gives 7 pens to Kate, they will have the same amount of pens. How many pens does Kate have? ___ pens

Answer 1

Kate has 50 pens.

Explanation:

If Jimmy gives 7 pens to Kate, that means Kate got 7 pens from Jimmy. Let the number of pens Jimmy and Kate have be `P_j` and `P_k` respectively.

From the question, we can deduce that

`P_j=P_k*128%rarr`equation 1

`P_j-7=P_k+7rarr`equation 2

From equation 1,

`P_j=1.28P_k`

From equation 2,

`P_j=P_k+14`

Since `P_j=P_j`,

`1.28P_k=P_k+14`

Hence,

`0.28P_k=14`

Solve,

`P_k=50`

Answer 2

Kate had `50` pens.

Explanation:

Kate must have had `14` pens less that Jimmy, because when his number of pens is reduced by `7` it is the same as the number of Kate's pens increased by `7`.

Let the number of Kate's pens be `x`, this represents `100%`

The number of Jimmy's pens is therefore `x+14` which is `128%` of the number of Kate's pens.

Compare the numbers and percents using direct proportion:

`x/(x+14) = 100/128 " "(larr "Kate")/(larr"Jimmy")`

Cross-multiply to get the equation:

`128x=100(x+14)`

`128x = 100x +1400`

`28x = 1400`

`x = 1400/28`

`x = 50`

Kate had `50` pens.

Check:

`50+14 = 64`

`64/50 xx100% = 128%`

Or: `64-7 = 50+7=57`

`14/50 xx 100% = 28%`