How to do this question?

Question

Please provide the explaination.... =)

Mavis and Janice have some beads each. If Mavis gives Janice 60 beads, she will have 4times as many as Janice. If mavis gives 300 beads to Janice, she will have 1.5 times as many beads as Janice. How many beads does Mavis have at first?

I've tried drawing a model but it still is'nt clear! Please help! Thanks! =D

Answer 1

Let Mavis has x bears and Janice has y bears

After the first change          x-60=4(y+60)

After the second change      x-300=1.5(y+300)

x=1020    and y=180

Answer 2

Let M be the number of beads Mavis has.

Let J be the number of beads Janice has.

Equation 1:

"If Mavis gives Janice 60 beads, she will have 4 times as many as Janice."

(M - 60) = 4(J + 60)

Solve for M:

M - 60 = 4J + 240

M = 4J + 300

Equation 2:

"If Mavis gives 300 beads to Janice, she will have 1.5 times as many beads as Janice."

(M - 300) = 1.5(J + 300)

Solve for M:

M - 300 = 1.5J + 450

M = 1.5J + 750

Now equate these, to eliminate M:

4J + 300 = 1.5J + 750

2.5J = 450

5J = 900

J = 900/5

J = 180

Now plug in J = 180 to solve for M.

M = 4J + 300

M = 4(180) + 300

M = 720 + 300

M = 1020

Answer:

Mavis has 1,020 beads

Janice has 180 beads

Double-check:

If Mavis gives away 60 beads she'll have 960 and Janice will have 240.  That is 4 times as much.

If Mavis gives away 300 beads she'll have 720 and Janice will have 480.  That is 1.5 times as much.