Multi step problem solving

Question

Myra has some oranges to share among 3 friends. Jennifer gets half and 3 more. Angela gets half the remainder and 3 more. Josie gets half the remainder plus 3. Myra has 10 oranges left. How many did she have at the start?

Answer 1

Let M=number of oranges Myra had

J=number of oranges Jennifer gets

A=number of oranges Angela gets

S=number of oranges Josie gets

J=M/2+3    REMAINDER IS M-(M/2+3)=M/2-3=(M-6)/2=(2M-12)/4

A=(M-6)/4+3=(M+6)/4  REMAINDER IS (M-18)/4=(2M-36)/8

S=(M-18)/8+3  REMAINDER IS (M-18)/8-3=(M-42)/8=10 REMAINING TO MYRA

M-42=80 M=122

J=64

A=32

S=16

J+A+S=112 LEAVING 10 FOR MYRA

 

Answer 2

let x = the number of oranges Myra has at beginning.

Jen gets .5x+3 ... remainder, left with Myra now is x-.5x-3, .5x-3

Angela gets 0.5*(.5x-3)+3 = .25x-1.5+3 = .25x+1.5 ... now, Myra has .5x-3-.25x-1.5 = .25x-4.5

Josie gets 0.5*(.25x-4.5)+3 = 0.125x-2.25+3 = 0.125x+.75 ... now Myra has .25x-4.5-0.125x-.75=

0.125x-5.25

0.125x-5.25 = 10 (left with Myra after distribution to Jen, Angela and Josie)

0.125x=15.25

x= 122

 

Jen got 64, Angela got 32, Josie got 16 ... leaving 10 for Myra!!!!

 

You can also solve by using the formula for geometric sequences, but I won't try.  The "slow and sure" method is clearest for how one would solve such problems.

Answer 3

Hi Lavana;

They are correct.