SOLUTION: In Katy's garden there are 15 ladybugs. They are increasing at 2 ladybugs per month. there are currently 175 aphids and the number of aphids is decreasing at 3 aphids per month.

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Question 829307: In Katy's garden there are 15 ladybugs. They are increasing at 2 ladybugs per month. there are currently 175 aphids and the number of aphids is decreasing at 3 aphids per month. When will the number of ladybugs and aphids in Katy's garden be the same? Thank you in advance for any help!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
Some thought should give you how to see this is a system of linear equations, two variables.

x=0 for time NOW. Number of bugs is y, and number of months is x.

Ladybugs: slope is 2 and y intercept is 15. The equation is .

Aphids: slope is . The y intercept is 175. The equation is .

WHEN do these two equations have the same point, or, what is the intersection point?

SOLVE FOR x.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

In Katy's garden there are 15 ladybugs. They are increasing at 2 ladybugs per month. there are currently 175 aphids and the number of aphids is decreasing at 3 aphids per month. When will the number of ladybugs and aphids in Katy's garden be the same? Thank you in advance for any help!


Let months for them to be same be M

Then equation for ladybugs = 15 + 2M

Equation for aphids = 175 – 3M



They are the same number when: 15 + 2M = 175 – 3M

2M + 3M = 175 – 15

5M = 160

M, or number of months until they’re the same number = , or 

You can do the check!! 



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