Answer: it will take Paul 11 months to have $2,000 in his account, assuming he does not withdraw any money or make any additional deposits.
Explanation:
Let x be the number of months that Paul has deposited money into his account. The total amount of money he deposits can be represented by the equation y = 150x, where y is the total amount of money in his account after x months.
To find the value of y after 6 months, we can substitute x = 6 into the equation:
y = 150(6) = 900
However, we know that the actual amount of money in Paul's account after 6 months is 1,250. This means that he must have earned interest on his deposits.
To account for the interest, we can add a constant term to the equation, representing the amount of interest earned. Let's call this constant term b. Then the equation becomes:
y = 150x + b
We know that when x = 6, y = 1,250. We can use this information to solve for b:
1,250 = 150(6) + b
b = 1,250 - 900
b = 350
So the equation that represents the total amount of money Paul deposits into his account is:
y = 150x + 350 (in point slope form, this is y - 350 = 150(x - 0)).
To find the number of months it will take for Paul to have $2,000 in his account, we can set y = 2,000 in the equation and solve for x:
2,000 = 150x + 350
1,650 = 150x
x = 11
Therefore, it will take Paul 11 months to have $2,000 in his account, assuming he does not withdraw any money or make any additional deposits.