Meiling and Meimei divide $69 into 2 shares. 3/4 of Meiling's share is equal to 2/5 of Meimei's share. How much does each get?

L + M = 69

so,
L = 69-M

3/4 (69-M) = 2/5 M
or,
15(69-M) = 8M
1035 - 15M = 8M
23M = 1035
M = 45

So, Meimei had $45
and Meiling had $24

3/4 of 24 = 18
2/5 of 45 = 18

To solve this problem, let's first assign variables to represent the shares of Meiling and Meimei.

Let's say Meiling's share is represented by "M" and Meimei's share is represented by "N."

According to the problem, we know that:

The total amount divided is $69, so we can create an equation: M + N = 69 --(1)

We are also given that 3/4 of Meiling's share is equal to 2/5 of Meimei's share. This can be represented mathematically as:

(3/4)M = (2/5)N

To eliminate the fractions, we can multiply both sides of the equation by the least common denominator (LCD) of 4 and 5, which is 20.

20 * (3/4)M = 20 * (2/5)N

15M = 8N --(2)

So now we have two equations:

M + N = 69 --(1)
15M = 8N --(2)

To solve this system of equations, we can use a method called substitution or elimination.

Let's use the elimination method to solve this system of equations. We will multiply equation (1) by 8 and equation (2) by 5 to make the coefficients of N the same:

8 * (M + N) = 8 * 69
5 * (15M) = 5 * 8N

Simplifying these equations gives us:

8M + 8N = 552 --(3)
75M = 40N --(4)

Now, let's eliminate N by multiplying equation (4) by 2 and equation (3) by 5:

10 * (8M + 8N) = 10 * 552
5 * (75M) = 5 * 40N

Simplifying these equations gives us:

80M + 80N = 5520 --(5)
375M = 200N --(6)

Now, subtract equation (6) from equation (5) to eliminate N:

80M + 80N - 375M = 5520 - 200N

Combining like terms:

-295M + 80N = 5520 - 200N

Moving all the terms involving N to one side and all the terms involving M to the other side:

80N + 200N = 5520 + 295M

Simplifying:

280N = 295M + 5520

Now, we can divide both sides by 5:

56M = 59N + 1104

To find whole number solutions for M and N, we need to look for integer solutions that satisfy this equation. We can start by substituting small values for one variable and solving for the other.

Let's assume M = 4:

56(4) = 59N + 1104
224 = 59N + 1104
59N = -880
N = -880/59

Since N should represent a share, it cannot be negative. Thus, assuming M = 4 doesn't give a valid solution.

Let's try assuming N = 4:

56M = 59(4) + 1104
56M = 236 + 1104
56M = 1340
M = 1340/56
M = 67/3

Since M should represent a share, it cannot be a fractional value. Thus, assuming N = 4 doesn't give a valid solution either.

This means that the problem does not have a whole number solution that satisfies both equations. It is possible that there was an error in the problem statement or some information is missing.

take x as meilings share while take meimei share as y

first equation
x+y=69
now make x or y as the subject so i'll make x as subject so
x=69-y
now we will make an second equation in which we will considey x as(69-y)
second equation
3/4x + 2/5y=69
3/4(39-y)+2/5y=69
39-y+2/5y=92
take 5 as lcm
195-5y

I hate all of you