Word Problem help please asap?
sami is a veterinarian at a zoo. Over a yr she treats 23 birds and raccoons w/ a total of 58 legs. HOw many birds does she treat? (Trying to help my kid w/math problem and I am having a brain moment can can't remember the formula to do this....)
Comments
Hello!
There isn't a special formula for this kind of problem. But you can boil it down to a problem with two variables in two equations and solve them; with X the number of birds and Y the number of raccoons:
equation 1: X + Y = 23 (The total number of animals is 23)
equation 2: 2X + 4Y = 58 (There are 58 legs to be found, 2 on each bird and 4 on each raccoon)
Then eliminate one variable (X in this case, but you could eliminate Y just as well) by transforming the first equation and inserting it in the second:
X = 23 - Y inserted in 2X + 4Y = 58 gives you:
2 x (23 - Y) + 4Y = 58
46 - 2Y + 4Y = 58 |-46
2Y = 12 |/2
Y = 6 meaning there are 6 raccoons.
use that in X = 23 - Y and you get
X = 23 - 6 = 17 so there are 17 birds.
Quick Test:
17 birds x 2 legs = 34 legs
plus 6 raccoons x 4 legs = 24 legs
equals 58 legs in total.
If all the equations confuse you, then I can offer a more visual approach for this problem:
Suppose there were 23 two-legged creatures treated, then you would have 46 legs of the 58 covered. This means, there are 58 - 46 = 12 legs uncovered. Now you have to distribute these 12 leftover-legs on some two-legged creatures to make them four-legged ones. As you can add 2 legs per creature, there must be 12 / 2 = 6 four-legged animals.
This leaves 23 - 6 = 17 two-legged birds plus 6 four-legged raccoons.
Test:
17 birds x 2 legs = 34 legs
plus 6 raccoons x 4 legs = 24 legs
equals 58 legs in total.
Hope that helped, good luck in the future!
b + r = 23: eqn 1
4b +2r = 58: eqn 2
2b + 2r = 46: 2*eqn 1
2b = 12: eqn2 - 2* eqn 1
b = 6
r = 23-6 = 17