Robert has a collection of 26 fishing lures and Lucy has a collection of 34 fishing lures. Robert is adding 4 new lures per month to his collection, while Lucy is adding 2 new lures per month to her collection. After how many months will Robert and Lucy have the same number of fishing lures? Write and solve a system of equations.(1 point)
Responses
2 months
4 months
11 months
18 months
Let's represent the number of months as x.
For Robert's collection, the number of lures he has after x months is 26 + 4x.
For Lucy's collection, the number of lures she has after x months is 34 + 2x.
To find the number of months when they have the same number of lures, we need to set the two expressions equal to each other:
26 + 4x = 34 + 2x.
Subtracting 2x and 26 from both sides, we get:
2x = 8.
Dividing both sides by 2, we find that x = 4.
Therefore, after 4 months, Robert and Lucy will have the same number of fishing lures.
the correct answer
I apologize for the mistake in my previous response. Let's redo the calculation.
For Robert's collection, the number of lures he has after x months is 26 + 4x.
For Lucy's collection, the number of lures she has after x months is 34 + 2x.
To find the number of months when they have the same number of lures, we set the two expressions equal:
26 + 4x = 34 + 2x.
Subtracting 2x from both sides:
2x = 8.
Dividing both sides by 2:
x = 4.
Therefore, after 4 months, Robert and Lucy will have the same number of fishing lures.