SOLUTION: In Katy's garden there are 105 ladybugs. They are increasing at two ladybugs per month. There are currently 175 aphids and the number of aphids is decreasing at three aphids per mo

Algebra ->  Equations -> SOLUTION: In Katy's garden there are 105 ladybugs. They are increasing at two ladybugs per month. There are currently 175 aphids and the number of aphids is decreasing at three aphids per mo      Log On


   

Question 1068012: In Katy's garden there are 105 ladybugs. They are increasing at two ladybugs per month. There are currently 175 aphids and the number of aphids is decreasing at three aphids per month. When will the number of ladybugs and aphids in Katy's garden be the same?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
there are 105 ladybugs.

they are increasing 2 each month.

let y = number of ladybugs.

let x = number of months.

formula for number of ladybugs is y = 2x + 105.

there are 185 aphids and their number is decreasing by 3 per month.

let y = number of aphids.

let x = number of months.

formula for number of aphids is y = -3x + 175.

solve these 2 equations simultaneously and you will find when the number of ladybugs is equal to the number of aphids.

the equations that need to be solved simultaneously are:

y = 2x + 105
y = -3x + 175

when the value of y for the ladybugs is the same as the value of y for the aphids, your answer.

subtract the second equation from the first to get:

0 = 5x - 175

add 175 to both sides of this equaiton to get:

175 = 5x

solve for x to get x = 14.

in 14 months, the number of ladybugs and aphids will be the same.

that number will be 133.

2*14 + 105 = 28 + 105 = 133

-3*14 + 175 = -42 + 175 = 133

your solution is that the number will be the same in 14 months.