Hi, if you insist on using models only, i am not sure if you might find the following useful.

But i shall share my solutions, hoping they be useful to any others reading this forum.

[Allow me also to comment that solutions that are mathematically correct should be allowed... i have heard kids saying their teachers "insist" on solving their problems certain ways only... my feeling is that these teachers are stifling the kids so affecting their interests in mathematics.]

1) Joseph has some local and foreign stamps in 2 boxes. In Box A, the numbers of local and foreign stamps are in the ratio 3: 4. In Box B, the number of local stamps is twice the number of foreign stamps. Joseph transfers half of the foreign stamps from Box A to Box B. The numbers of stamps in Box A become 105 and the ratio of the number of local stamps to the number of foreign stamps in Box B becomes 6:5.

a) How many foreign stamps have been transferred from Box A to Box B?

b) What is the number of stamps in Box B at first?

Solution:

..............................box A........................box B

........................local.....foreign.......local.....foreign

at 1st:................3u..........4u.............2p.........1p.........................[where 'u' represents 'unit' and 'p' represents 'part']

transfer:..........................-2u.........................+2u

in the end:........3u..........2u.............2p......1p+2u

total in box A = 5u = 105 stamps

therefore, .........1u = 105 / 5 = 21 stamps

(a) no. of foreign stamps transferred from A to B = 2u = 42. (ANS)

Now, in the end, in box B, the ratio of local : foreign = 6 : 5

so, the 2p = 6 pn.......................................['pn' represents 'portion']

thus, ....1p = 3 pn

so that, 2u = 2 pn [because 1p + 2u = 5 pn],

and so, 1 pn = 1u

At first, there are 3p stamps in box B, which is equal to 9u.

(b) therefore, there are 9 x 21 = 189 stamps in box B at first. (ANS)

2) Ravi had a total of 80 pieces of $10 notes and $50 notes. He used ½ of his $10 notes and withdrew another four pieces of $50 notes from the bank. After which, the number of $50 notes he had was 2/5 the number of $10 notes. Find the total value of the 80 pieces of notes he had at first.

Solution:

.......no. of...........$10................$50

at 1st:...................2u..................1p............total = 80, means that 2u + 1p = 80, or 1p = 80 - 2u........(1)

change:...............-1u.................+4

in end:.................1u................1p+4

ratio is:..................5........ : ........2

which means that 2u = 5p + 20

using (1), ............2u = 5(80 - 2u) + 20

therefore,.........12u = 420

that is, ..............1u = 35, and from (1), 1p = 80 -70 = 10

therefore, value of 80 pieces at first = 70 x $10 + 10 x $50 = $1200. (ANS)

3) 2/9 of Rani’s balloons were red and the rest were green. She gave away 15 green balloons and bought another 25 red balloons. She then had the same number of red and green balloons. How may green balloons did she have at first?

Solution:

.................................red................green

at first:.......................2u..................7u

change:...................+25.................-15

in end:...................2u + 25..........7u - 15

she had same no. of each in the end, so, 2u + 25 = 7u - 15

that is, .........5u = 40 balloons

so that, ........1u = 8 balloons

therefore, she had 7 x 8 = 56 green balloons at first. (ANS)