Arielle has a collection of grasshoppers and crickets. She has 561 insects in all. The number of grasshoppers is twice the number of crickets. Find the number of each type of insect that she has.
2007-11-06 10:12:12 · 25 answers · asked by ohmygoditsanne 1 in Education & Reference ➔ Homework Help
Let x represent the number of each insect
2x+x = 561
3x = 561
x = 561 / 3
x = 187
there are 187 crickets and 2(187) grasshoppers
2007-11-06 10:16:45 · answer #1 · answered by safbmt 1 · 1⤊ 0⤋
Divide 561 3 ways because you are looking for three equal parts wherein you have a 2 to 1 ratio or 1 set of insects is twice as many as the other. Therefore Divide 3 into 561 and you get 187. Twice 187 and you get the number of grasshoppers (374 grasshoppers) and 1X 187 = (187 crickets) . You can check your answer by adding 374+187 and you will get 561 again.
Hope that helped.
2007-11-06 18:35:49 · answer #2 · answered by #1 Mom 2 · 0⤊ 0⤋
You'll need to mae a system of 2 equations, with 2 variables each. Let's call the # of crickets C and the # of grasshoppers G.
The problem tells you taht the total number of insects is 561, so C + G = 561. That's your first equation.
It also says that the number of grasshoppers, G, is equal to two times the number of crickets, C. So, G = 2C
Now, you can use method called substitution. You know that G is the same as 2C. So, you can put 2C in the other equation in the same place as C. So: C +2C = 561.
Now, solve this equation for C. It's just simple algebra. You end up with 187 as C.
Then, once you have C, use the other equation to find G. Plug 187 into the equation: G = 2*187, or G = 374.
So, the number of grashoppers is 374 and the number of crickets is 187.
2007-11-06 18:19:38 · answer #3 · answered by FantasyGeek 4 · 1⤊ 0⤋
set up the probelm. crickets=x, grasshoppers=2x, total bugs is 561.
solve the equation for x.
2x+x=561
3x=561
x= 187.
now you know x, which is the number of crickets. # of crickets =187.
now, there a couple of ways you can find the number of grasshoppers. the easy way is to multiply 187 by 2 for a total of 374. or you can simply subtract 187 from 561, which also equals 374. The more complicated way is to plug 187 back into the equation. this would look like 187 times 2 + 187=561,
so 374+187=561 prooves this a true statement as well.
2007-11-06 18:25:13 · answer #4 · answered by vwj73 3 · 0⤊ 0⤋
Well, if the number of grasshoppers is twice the number of crickets then your number sentence would be 3x=561 or 561divided by three, which is 187. So that would be 187 crickets and 374 grasshoppers because twice of 187 is 374 and 374+187=561 which is the same number you started with. I hope you can understand that.
2007-11-06 18:20:29 · answer #5 · answered by pudgy_bunny 2 · 0⤊ 0⤋
divide 561 by 3 which is 187.. this way you know theres 187 crickets and since theres twice as many grasshoppers theres 374 grasshoppers
187 crickets
+374 grasshoppers
= 561 insects
2007-11-06 18:16:22 · answer #6 · answered by Pineapple 3 · 0⤊ 0⤋
You could either use a whole bunch of equations or just divide 561 by 3. It = 187
That means 187 x 2 = 374 grasshoppers
187 crickets
2007-11-06 18:21:37 · answer #7 · answered by Anonymous · 0⤊ 0⤋
She has 371 grasshoppers and 187 crickets. to figure it out you do x for crickets and 2x for grasshoppers. the equasion would be x + 2x = 561 then solve so combine like terms 3x=561 devide by 3 then x=187 so she has 187 crickets then 2x or 2 x 187 = 371.
2007-11-06 18:28:52 · answer #8 · answered by Alysha 1 · 0⤊ 0⤋
Grasshoppers times two equals the number of crickets
2G +C=561
2007-11-06 18:16:29 · answer #9 · answered by redunicorn 7 · 0⤊ 1⤋
G + C = 561
therefore.. C=561-G
2C=G
substitute
C=561- 2C
add 2C
3C=561
divide by 3
C=187
for G substitute the C in the original equation (2c=g)
2(187)=G
G=374
2007-11-06 18:22:06 · answer #10 · answered by Anonymous · 0⤊ 0⤋