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The average number of Peter's stickers and Jordan's stickers is 924. Peter has 232 more stickers than Jordan. Albert has 172 stickers more than Peter. What fraction of Albert's stickers are Jordan's stickers? Write your answer in its simpliest form

 Dec 29, 2021
 #1
avatar+35318 
+1

p + j = 924 (2) = 1848

p = j + 232         so p = 1040     and j = 808

 

a = p + 172 = 1212

 

j / a = 808 / 1212   = 2/3

 Dec 29, 2021
 #2
avatar+318 
+1

Let,

     a = Peter's sticker

     b = Jordan's sticker

     c = Albert's sticker

Given:

    1) \({a + b \over 2} = 924\) (average number of Peter's & Jordan's stickers)

         a + b = 2(924)

         a + b = 1848 (1)

     2)

         a = b + 232 => a - b = 232 (232)

     3) 

         c = a + 172 (3)

Solve for a using eq. (1) & (2), eliminate b

               a + b = 1848

            + a - b = 232

                    2a = 2080

                    2a/2 = 2080/2

                      a = 1040

Find b.                                    Find c.

        a + b = 1848                        C = a + 172

              b = 1848 - a                       = 1040 + 172

                 = 1848 - 1040             C = 1212

              b = 808

So,

      \( {Jordan’s stickers \over Albert’s stickers} = {b \over c} = {808 \over 1212}\)

                                         = 0.6666. . .

        Change 0.6666... to fraction.

                     x = 0.6666 . . .

                 10x = 6.6666 . . .

                -    x = 0.6666 . . .

                   9x = 6

                     x = 6/9 = 2/3

Therefore,

Jordan's stickers is 2/3 of Albert's stickers.

                    2/3 * 1212 = 808 ✓

 Dec 30, 2021

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