Tom has a collection of 30 CDs, and Nita has a collection of 18 CDs. Tom is adding 1 CD per month to his collection, while Nita is adding 5 CDs per month to her collection. After how many months will Tom and Nita have the same number of CDs? Write and solve a system of equations. (1 point) Responses 1 month 3 months 2 months 33 months
Let's assume that after x months, Tom and Nita have the same number of CDs.
After x months, Tom will have 30 + x CDs and Nita will have 18 + 5x CDs.
Setting the two equations equal, we have:
30 + x = 18 + 5x
Simplifying:
30 - 18 = 5x - x
12 = 4x
Dividing both sides by 4:
12/4 = x
3 = x
So, after 3 months, Tom and Nita will have the same number of CDs.
Therefore, the correct answer is 3 months.
Kendra owns a restaurant. She charges $3.00 for two eggs and one piece of toast and $1.80 for one egg and one piece of toast. How much does Kendra charge per egg? How much per piece of toast? Write and solve a system of equations. (1 point) Responses $1.20 per egg; $0.60 for toast $1.20 per egg; $0.60 for toast $0.60 per egg; $1.20 for toast $0.60 per egg; $1.20 for toast $0.60 per egg; $0.60 for toast $0.60 per egg; $0.60 for toast $1.20 per egg; $1.20 for toast
Let's assume the cost of one egg is x dollars and the cost of one piece of toast is y dollars.
According to the given information, we have the following system of equations:
2x + y = 3 --> equation 1 (The cost of two eggs and one toast is $3.00)
x + y = 1.80 --> equation 2 (The cost of one egg and one toast is $1.80)
We can solve this system of equations by using the method of substitution or elimination.
Using the method of substitution:
From equation 2, we have y = 1.80 - x. Substitute this value of y into equation 1:
2x + (1.80 - x) = 3
2x + 1.80 - x = 3
Combine like terms:
x + 1.80 = 3
Subtract 1.80 from both sides:
x = 3 - 1.80
x = 1.20
Now, substitute the value of x back into equation 2 to find y:
1.20 + y = 1.80
Subtract 1.20 from both sides:
y = 1.80 - 1.20
y = 0.60
Therefore, Kendra charges $1.20 per egg and $0.60 per piece of toast.
Therefore, the correct answer is $1.20 per egg; $0.60 for toast.