Joelle currently has 18 rocks in her 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. (6 points)
a) Joelle has y = _ x + _
b) Lewis has y = _ x + _
c) After how many weeks will Joelle and Lewis have the same number of rocks in their collections?
_ weeks
d) How many rocks will Joelle and Lewis have when the amount of rocks in their collection is equal? They will each have _ rocks in their collection.
Word bank:
3
65
66
30
2
70
12
4
18
a) Joelle has y = 4x + 18 (She currently has 18 rocks and gains 4 each week)
b) Lewis has y = 3x + 30 (He currently has 30 rocks and gains 3 each week)
c) To find when they will have the same number of rocks, we set the equations equal to each other: 4x + 18 = 3x + 30
Subtract 3x from both sides: x + 18 = 30
Subtract 18 from both sides: x = 12
So, after 12 weeks, Joelle and Lewis will have the same number of rocks.
d) To find the number of rocks they will each have at that time, we substitute x = 12 into either equation:
Joelle: y = 4 * 12 + 18 = 48 + 18 = 66 rocks
Lewis: y = 3 * 12 + 30 = 36 + 30 = 66 rocks
So, when they have the same number of rocks in their collection, they will each have 66 rocks.
a) Joelle has y = 4x + 18
Explanation: The initial number of rocks that Joelle has is 18 (y-intercept) and she gains 4 rocks each week (slope is 4).
b) Lewis has y = 3x + 30
Explanation: The initial number of rocks that Lewis has is 30 (y-intercept) and he gains 3 rocks each week (slope is 3).
c) To find out the number of weeks it would take for Joelle and Lewis to have the same number of rocks, we can set their equations equal to each other.
4x + 18 = 3x + 30
Simplifying the equation, we get:
x = 12
Therefore, it will take 12 weeks for Joelle and Lewis to have the same number of rocks in their collections.
d) To find out how many rocks Joelle and Lewis will have when their collections are equal, we can substitute the value of x (12 weeks) into either of the equations.
Using the equation for Joelle:
y = 4x + 18
y = 4(12) + 18
y = 48 + 18
y = 66
Therefore, when Joelle and Lewis have the same number of rocks in their collections, they will each have 66 rocks.
a) Joelle has y = 4x + 18, where x represents the number of weeks.
To set up this equation, we know that Joelle starts with 18 rocks, and she gains 4 rocks each week. The equation y = 4x represents the number of rocks she gains after x weeks. Adding her starting number of rocks, the equation becomes y = 4x + 18.
b) Lewis has y = 3x + 30, where x represents the number of weeks.
Similarly, Lewis starts with 30 rocks, and he gains 3 rocks each week. The equation y = 3x represents the number of rocks he gains after x weeks. Adding his starting number of rocks, the equation becomes y = 3x + 30.
c) To find out how many weeks it will take for Joelle and Lewis to have the same number of rocks in their collections, we need to set their equations equal to each other and solve for x.
Setting up the equation:
4x + 18 = 3x + 30
By rearranging the equation to isolate x, we get:
4x - 3x = 30 - 18
Simplifying further:
x = 12
Therefore, after 12 weeks, Joelle and Lewis will have the same number of rocks in their collections.
d) To find out how many rocks Joelle and Lewis will have when their collections are equal, we can substitute the value of x (12 weeks) into either equation and solve for y.
Using the equation y = 4x + 18, we substitute x = 12:
y = 4(12) + 18
y = 48 + 18
y = 66
Therefore, when their collections are equal after 12 weeks, Joelle and Lewis will each have 66 rocks in their collection.