SOLUTION: Blue stickers were sold in packet of 15 each. Green stickers were sold in packets of 40 each. Renee bought 5 packets of blue stickers and some packets if green stickers. Fatimah

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Question 1184735: Blue stickers were sold in packet of 15 each. Green stickers were sold in
packets of 40 each. Renee bought 5 packets of blue stickers and some
packets if green stickers. Fatimah bought 13 packets of blue stickers and
some packets of green stickers. Both girls bought the same total number of
packets of stickers.
(a) How many more green stickers did Renee buy than Fatimah
(b) After Renee used 3/5 of her green stickers and Fatimah used half of
her green stickers, they both had 452 green stickers left altogether.
How many blue and green did Fatimah buy altogether?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
x = number of packets of blue stickers.
y = number of packets of green stickers.

there are 15 blue stickers in one packet.
there are 40 green stickers in one packet.

renee bought 5 packets of blue stickers and come packets of green stickers.
fatimah bought 13 packets of blue stickers and some packets of green stickers.

both girls bought the same total number of packets of stickers.

(a) How many more green stickers did Renee buy than Fatimah.

renee bought 5 blue plus x green packets.
fatimah bough 13 blue plus y green packets.

they both bought the same number of packets.
you get:

5 + x = 13 + y

solve for x to get:

x = y + 8

this says that renee bought 8 more packets of green stickers than fatimah.

since there are 40 green stickers in a packet, then renee bought 8 * 40 = 320 more green stickers than fatimah.

(b) After Renee used 3/5 of her green stickers and Fatimah used half of
her green stickers, they both had 452 green stickers left altogether.
How many blue and green did Fatimah buy altogether?

the number of green stickers that renee had was 40 * (x + 8).
the number of green stickers that fatimah had was 40 * x.

after renee used 3/5 of her green stickers, she had 2/5 * 40 * (x + 8) left.
after fatimah used 1/2 of her green stickers, she had 1/2 * 40 * x left.

the total green stickers left was 452.

2/5 * 40 * (x + 8) + 1/2 * x = 452
simplify to get:
2/5 * 40 * x + 2/5 * 40 * 8 + 1/2 * 40 * x = 452
simplify to get:
16 * x + 16 * 8 + 20 * x = 452
combine like terms to get:
36 * x + 128 = 452
subtract 128 from both sides to get:
36 * x = 324
solve for x to get:
x = 9

renee had 9 + 8 = 17 packets of green stickers.
fatimah had 9 packets of green stickers.

total number of packets for renee were 9 + 17 = 22
total number of packets for fatimah were 13 + 9 = 22

they both had the same number of packets.
this is good.

renee had a total of 17 * 40 = 680 green stickers.
fatimah had a total of 9 * 40 = 360 green stickers.
renee had 680 - 360 = 320 more green stickers than fatimah.

renee had 2/5 of her green stickers left.
fatimah had 1/2 of he green stickers left.

2/5 * 680 = 272
1/2 * 360 = 180

the total number of green stickers left was 272 + 180 = 452.

everything appears to check out.

the questions and your solutions are:

(a) How many more green stickers did Renee buy than Fatimah

renee had 320 more green stickers than fatimah.


(b) After Renee used 3/5 of her green stickers and Fatimah used half of
her green stickers, they both had 452 green stickers left altogether.
How many blue and green did Fatimah buy altogether?

fatimah bought 13 packets of blue stickers and 9 packets of green stickers.
13 * 15 = 195 blue stickers
9 * 40 = 360 green stickers
total number of stickers that fatimah bought werre 555.

i checked the solution out and it looks good.
give it a try.
let me know how you did.

theo






Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Blue stickers were sold in packet of 15 each. Green stickers were sold in
packets of 40 each. Renee bought 5 packets of blue stickers and some
packets if green stickers. Fatimah bought 13 packets of blue stickers and
some packets of green stickers. Both girls bought the same total number of
packets of stickers.
(a) How many more green stickers did Renee buy than Fatimah
(b) After Renee used 3/5 of her green stickers and Fatimah used half of
her green stickers, they both had 452 green stickers left altogether.
How many blue and green did Fatimah buy altogether?
Green stickers are sold in packets of 40 each. 
Let number of packets of green stickers Renee and Fatimah bought, be G and F, respectively
Then Renee bought 40G green stickers and Fatimah bought 40F green stickers

Since both bought the same TOTAL number of packets, then we get: 5 + G = 13 + F
                                                                     G = F + 8 
As seen above, Renee bought F + 8 green packets, or 8 more green packets, or 8(40) = 320 more stickers than Fatimah.


After using  of her green stickers, Renee was left with:  green stickers 
After using ½ of her green stickers, Fatimah was left with: ½ * 40F, or 20F green stickers 

Since they ended up with a total of 452 green stickers, we can say that: 16F + 128 + 20F = 452
16F + 20F = 452  -  128
36F = 324
F, or number of packets of green stickers Fatimah bought = 
Number of packets of green stickers Renee bought = 9 + 8 = 17

Sold in packets of 15 each, Renee bought 5 packets, or 15(5) = 75 blue stickers
Sold in packets of 15 each, Fatimah bought 13 packets, or 15(13) = 195 blue stickers

Sold in packets of 40 each, Renee bought 17 packets, or 40(17) = 680 green stickers
Sold in packets of 40 each, Fatimah bought 9 packets, or 40(9) = 360 green stickers

Number of stickers bought, altogether: 75 + 195 + 680 + 360 = 1,310
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