C = cats
D = dogs
M = mice
1(C) + 15D + .25M = 100 or
4C + 60D + M = 400 (1)
Also, C + D + M = 100 (2)
Subtracting (1) from (2) yields 3C + 59D = 300
Dividing through by the lowest coefficient yields
C + 19D + 2D/3 = 100
Let 2D/3 = an integer "k" making D = 3k/2
Substituting, 3C + 88.5k = 300 yielding C = 100 - 29.5k
"k" must be even and can only be 2 making C = 100 - 59 = 41 from which D = 3 and m = 56.
41 + 45 + 14 = 100 animals
41(1) + 45(15) + 56/4 = $100
Will use the same notations, C,D and M for cats, dogs and mice, and with the same constraints where C,D and M must be integers.
From the cost,
from the number of animals,
C+D+M = 100......(2)
Since 56 and 3 are coprime, we can only have 3 dogs, 56 mice, or any multiple thereof.
However, 6 dogs and 112 mice would exceed the budget, so we go with
3 dogs, 56 mice, and are left with 41 cats.
So the solution is correct.
Thank you, that was the answer I got too, but in a slightly different method, but I want to learn for how you figure this out, with this problem. I feel like you just you the same method but I am having a little problem with this one:
"Suppose you want to make $5 using exactly 100 common US coins.Easy, you say: just use nickels (5 cents each). But I say, no - we have NO nickels, only pennies (1 cent), dimes (10 cents) and quarters (25 cents) - is it possible to make $5 now with exactly 100 of these coins? Why or why not?"
These problems belong to a class called diophantine equations. If these are what you are doing in class, they will be solved in a different way.
For linear algebra, I will solve it similar to the previous problem, as follows.
p=number of pennies
d=number of dimes
q=number of quarters
p+10d+25q=500...(1) (number of cents)
p+d+q=100 ....(2) (number of coins)
Subtract (2) from (1),
3d+8q = 400/3 ...(3)
It is evident that (3) has no solution in integers because we cannot have the sum of two integers to be a mixed fraction.
math,correction - Assume that each situation can be expressed as linear cost ...
Algebra 1- Math - The owner of a pet store spent $236 on 10 dogs and cats. The ...
maths - Scenario: There is a bus with 7 girls inside, Each girl has 7 bags, ...
Math - Two cats are taking a walk. 1 cat runs off. three cats come back. 1 cat ...
Essay Writing - I need help with making my outline parallel. II. Body A. Needs 1...
WITC math - There is a bus with 7 girls inside, Each girl has 7 bags, Inside ...
math - If there were only cats and dogs at the pound and the ratio of cats to ...
Algebra - Assume it costs Microsoft $4,300 to manufacture 7 Xbox 360s and $8,290...
Algebra - Determine if the relationship represented in the table is linear. If ...
algebra - Cupcakes cost $1.50 each to produce with fixed cost of $50. a) Express...