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Tommy had some pencils in Box A and 480 pencils in Box B. When he moved 10% of the pencils from Box B to Box A, the number of pencils in Box A increased by 30%. He then sold 75% of the pencils in Box A and gave away 75% of the remaining pencils in Box A. How many pencils were left in Box A in the end?

Jun 15, 2022

#1
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Let A be the number originally in  Box A

After he moved 10% of the pencils in B to A it  contained

A + .10 (480)  = 1.30 A

A + 48 =  1.30 A

48 = 1.30 A - A

48  = .30A

A = 48/.30   =   160

So......there were 160 + 48 =  208  pencils in the box after this

He sol 75%  of these...so

208 (.25) =  52 remained after this

And he gave   75%  of these away....so

52 (.25)  =  13 remained at the end   Jun 15, 2022
edited by CPhill  Jun 15, 2022
#2
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Let x = # of pencils in Box A originally

x + 480 (80%) = x + 30% x

48/0.3 = 0.3x/0.3

x = 160

* 160 + 48 = 208

* 208 (1 - 0.75) = 208 (0.25) = 52

* 52 (1 - 0.75) = 52 (0.25) = 13 pencils left

Jun 15, 2022