Question 1068012
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.