Question

four children,andrea,christain and martina,are collecting stamps.martina has twice as many as neil.andrea has two more thanneil and half as many as christain.between them they have 54 stamps.how many has each child

Answer 1

We can write this algebraically as A + N + C + M = 54

We also know that "Martina has twice as many as Neil." This means, M = 2N. No matter the number of stamps Neil (N) has, Martina (M) will have twice as many. Let's check: If Neil (N) has 20 stamps, then: M = 2(20) = 40. 40 = 40 and 40 is also twice that of 20. This equation is correct.

Lastly, we know that "Andrea has two more than Neil and half as many as Christian."
Let's break this up into two equations, as above.
Andrea has two more than Neil: A = N + 2 (if Neil has 4, Andrea has 6. This works.)
Andrea has half as many as Christian: A = (1/2)C (if Christian has 18, Andrea has 9. This works.)

So, we have the following equations:
A + N + C + M = 54
M = 2N
A = N + 2
A = (1/2)C

Now, we want to solve the last three equations for the same variable so that we can substitute them into the first equation (A + N + C + M = 54) and figure out how many one of the children has.

We know M = 2N.

A + N + C + (2N) = 54

We also know A = N + 2

(N + 2) + N + C + (2N) = 54

Now we just need to do something to C.
Of our other equations, we have A = N + 2 and A = (1/2)C. We can substitute so that:
N + 2 = (1/2)C (since they both equal A).
To isolate C, we can multiply both sides by 2 (the reciprocal of 1/2)

2(N + 2) = 2(1/2)C
2N + 4 = C distribute on the left, multiply 2*(1/2) on the right to isolate C

Now, in our main equation, we can substitute C:

(N + 2) + N + (2N + 4) + 2N = 54

When we simply and solve for N, we will know how many stamps Neil had.

N + 2 + N + 2N + 4 + 2N = 54
6N + 6 = 54 Combine like terms
6N = 48 Subtract 6 from both sides
N = 8 Divide both sides by 6

Neil had 6 stamps.

We can use the following equations we derived from the word problem before to figure out how many stamps the other children had:
M = 2N
A = N + 2
A = (1/2)C

Let's start with Andrea.

A = N + 2
A = 6 + 2
A = 8

Andrea had 8 stamps.

A = (1/2)C
8 = (1/2)C
16 = C

Christian had 16 stamps.

M = 2N
M = 2(6)
M = 12

Martina had 12 stamps.

In summary: Neil had 6 stamps, Andrea had 8 stamps, Christian had 16 stamps, and Martina had 12 stamps.