Bob saved five dollars in January $10 in February and $15 in March. If he continues this pattern, how much money will he save in a year?
Bob saved a total of $5 + $10 + $15 = $<<5+10+15=30>>30 in the first three months.
Since a year has 12 months, then Bob will save 12 x ($30/3) = 12 x $<<30/3=10>>10 = $<<12*10=120>>120. Answer: \boxed{120}.
To determine how much money Bob will save in a year, we need to calculate the total amount he saved in the three months and then extrapolate that to a full year.
In January, Bob saved $5.
In February, Bob saved $10.
In March, Bob saved $15.
To find the total amount saved in the first three months, we add the amounts together:
$5 + $10 + $15 = $30.
Since there are 12 months in a year, we need to determine how many sets of three months are in a year. This can be done by dividing 12 by 3:
12 / 3 = 4.
Now, we multiply the total amount saved in three months by the number of sets of three months in a year:
$30 * 4 = $120.
Therefore, if Bob continues saving in the same pattern, he will save $120 in a year.
To find out how much money Bob will save in a year, we need to determine the pattern of his savings and calculate the total for the entire year.
In this case, Bob saved $5 in January, $10 in February, and $15 in March. We can observe that the savings increase by $5 each month. So, the pattern is that Bob saves an additional $5 each month.
To calculate the total savings for the year, we need to consider the 12 months. From January to March, Bob saved a total of $5 + $10 + $15 = $30. Since Bob saves an additional $5 each month, he will save $15 in April, $20 in May, $25 in June, and so on.
To calculate the total savings for the rest of the months, we can use an arithmetic series formula:
Sum = (n/2) * (2a + (n-1)d)
Where:
n = number of terms (months in this case)
a = first term (amount saved in January, which is $5)
d = common difference (the increase in savings each month, which is $5)
Using this formula, the total savings for the remaining 9 months (April to December) can be calculated as:
Sum = (9/2) * (2 * $5 + (9-1) * $5)
= (9/2) * (2 * $5 + 8 * $5)
= (9/2) * (10 + 40)
= (9/2) * 50
= 9 * 25
= $225
Therefore, Bob will save an additional $225 from April to December.
To find the total savings for the entire year, we add the savings from January to March ($30) to the savings for the rest of the months ($225):
Total savings for the year = $30 + $225 = $255.
Bob will save a total of $255 in a year if he continues this pattern.