Answer:
A. 293 dolls each
B. 710 beads
C. (n+n)/3 >2xy
Explanation:
1. Let A be the number of dolls collected by Gelyn and B the number collected by Geraldine.
At the start:
A = 1,178, and
B = 588
Girlie gets the same number of dolls from both, which we'll say is x. The situation is then:
Gelyn: A - x
Geraldine = B - x
Girlie = 2x
After the transfer, we find that A-x = 3(B-x) [Gelyn had 3 times as many dolls left as Geraldine]
Lets rearrange this last expression:
A-x = 3(B-x)
A-x = 3B-3x
2x=3B-A
Use the values of A and B to find x:
2x=3(588)-(1,178)
2x = 586
x = 293
Gelyn and Geraldine each gave Girlie 293 dolls.
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2. Let A, B, and C stand for the number of beads in Boxes A, B, and C, respectively. We are told that:
A + B + C = 4342 [Box A, Box B, and Box C contain 4,342 beads altogether]
and learn that:
A+18 = B, and [There are 18 more beads in Box B than Box A]
C = 3B [There are 3 times as many beads in Box C as in Box B]
How many beads in Box A?
We have three equations. Lets find a way to substitute so that we can eliminate the unknowns B and C.
Look at: A + B + C = 4342
If we can rearrange the other equations to express the variables B and C in terms of A, we could solve the problem.
A+18 = B becomes B=A+18 [We can now calculate B from A]
The second, C = 3B, does not have A, but we can use the above expression for B, which will allow C to be expressed as a function of A:
C = 3B
C = 3(A+18)
C = 3A + 64 [We can now calculate C from A]
Use these definitions of B and C in the first equation (substitution):
A + B + C = 4342
A + (A+18) + (3A + 64) = 4342
6A + 82 = 4342
6A = 4260
A = 710 Box A has 710 beads
3. The sum of x and n divided by 3 more than twice the product of x times y
(n+n)/3 [The sum of x and n divided by 3]
>2xy [more than twice the product of x times y]
Put these together:
(n+n)/3 >2xy