Question

Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.

Set up a system of equations to show how many rocks each has in their collection.

Samuel has y= ___x+ ____

Lewis has ____ x+____.

After how many weeks will Samuel and Lewis have the same number of rocks in their collections? _____ weeks

How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have ____ rocks in their collection.

Answer 1

[AI-generated answer — Bot]

Samuel has y = 4x + 18 (y represents the number of rocks in his collection, x represents the number of weeks)

Lewis has y = 3x + 30

To find the number of weeks until they have the same number of rocks:
4x + 18 = 3x + 30
x = 12

After 12 weeks, they will have the same number of rocks in their collections.

To find out how many rocks they will each have:
Plug in x = 12 into either equation
Samuel: y = 4(12) + 18 = 66 rocks
Lewis: y = 3(12) + 30 = 66 rocks

They will each have 66 rocks in their collection when the amount is equal.

Answer 2

Solve the systems of equations.

3x + 2y = 2
-2x = y = 8