P6 Math: Malik and Bilal money

If Malik gives $42 to Bilal, Malik will have twice as much money as Bilal. If instead, Malik gives $12 to Bilal, Malik will have thrice as much money as Bilal. Find the ratio of Malik's money to Bilal's money at first

Solution:

Method 1

At first we solve it algebra method, since Primary 6 students start learning algebra.

There will be two equations from the problem:

(1) M - 42 = 2 (B + 42)

(2) M - 12 = 3 (B + 12)

Eliminate M with substitution method:

3(B+12) +12 - 42 = 2(B + 42)

B = 84 - 36 - 12 + 42 = 78

Find M from (1)

M = 282

So M:B = 282:78 = 47:13

Method 2

We develop a model

Carefully we can see in the second picture, the remaining blocks should be added up to make 1 unit too. That is, 30 + 30 + 30 = 90.

So 1 unit = 90.

Ben had 90 - 12 = $78 at first.

Malik had 3 x 90 + 12 = $282 at first.

Ratio is M:B = 282:78 = 47:13