Question

Daniel had 80 more stickers than Elle. He gave 1/4 of his stickers to Elle. She then gave 3/5 of her stickers to Daniel. In the end, Daniel had 92 more stickers than Elle. How many stickers did Daniel have at first? (please refrain from using algebra to solve this question as this is a primary 6 question thanks.)

Answer 1

Answer:

Daniel had 108 stickers at first

Step-by-step explanation:

Number of Daniel's stickers = d

Number of Elle's stickers = e

Since Daniel had 80 more stickers than Elle, d = 80 + e

e = d - 80

Daniel gave 1/4 of his stickers to Elle, Daniel is left with (d - d/4) = 3d/4

Elle now has e + d/4 = d - 80 + d/4 = (5d/4) - 80 = (5d - 320)/4

Elle now gave 3/5 of her remaining stickers to Daniel:

Elle now has:

$e_{new} = \frac{5d -320}{4} - \frac{3}{5} * \frac{5d -320}{4}\\\\e_{new} = \frac{5d -320}{4} - \frac{15d -960}{20}\\\\e_{new} = \frac{25d - 1600 - 15d + 960}{20} \\\\ e_{new} = \frac{10d-640}{20}$

Daniel now has:

$d_{new} = \frac{3d}{4} + \frac{3}{5} (\frac{5d - 320}{4} )\\d_{new} = \frac{3d}{4} + \frac{15d - 960}{20} \\d_{new} = \frac{30d - 960}{20}$

Daniel now had 92 more stickers than Elle

$d_{new} = E_{new} + 92$

$\frac{30d - 960}{20} = \frac{10d - 640}{20} + 92$

Multiply through by 20

30d - 960 = 10d - 640 + 1840

20d = -640 + 1840 + 960

20 d = 2160

d = 2160/20

d = 108