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

2 Answers
Evan
May 26, 2018

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#

EZ as pi
May 26, 2018

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%#

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