Jean has $280 in her savings account starting next week she will deposit $30 in her account every week is the amount of money in her account proportional to the number of weeks.
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How do you find out the answer I don’t get it I’m confused
To determine whether the amount of money in Jean's account is proportional to the number of weeks, we need to see if there is a constant ratio between the money and the number of weeks.
Let's denote the amount of money in Jean's account as M and the number of weeks as W.
According to the given information, Jean has $280 in her savings account initially, and she deposits $30 every week. We can represent this as follows:
M = 280 + 30W
Now, let's calculate the amount of money in Jean's account after different numbers of weeks:
For 1 week:
M = 280 + 30(1) = 310
For 2 weeks:
M = 280 + 30(2) = 340
For 3 weeks:
M = 280 + 30(3) = 370
From these calculations, we observe that the amount of money in Jean's account keeps increasing by $30 for each additional week.
Therefore, the amount of money in her account is proportional to the number of weeks, and the constant ratio is $30 per week.
To determine if the amount of money in Jean's account is proportional to the number of weeks, we can calculate the ratio of the amount of money in her account to the number of weeks.
Let's denote the amount of money in Jean's account as "M" and the number of weeks as "W". The ratio of the amount of money to the number of weeks can be expressed as M/W.
In this case, Jean has $280 in her account initially, and she will deposit $30 every week. So, the equation for the amount of money in her account can be written as:
M = 280 + 30W
This equation shows that the amount of money in Jean's account is not directly proportional to the number of weeks. The additional $30 that she deposits every week causes the amount of money to increase by a constant value, regardless of the number of weeks.
If the amount of money were directly proportional to the number of weeks, the equation would be M = kW, where "k" is a constant value. In this scenario, the equation would be linear, and the graph would be a straight line passing through the origin (0, 0). However, since Jean is depositing a fixed amount every week, the graph of her account balance over time would be a linear line with a positive slope, but it would not pass through the origin.
In conclusion, the amount of money in Jean's account is not directly proportional to the number of weeks due to her regular deposits.
Depending on the constant of proportionality, 280+30x is always proportional to x.
if x=1, 310 = 310x
If x=2, 340 = 170x
If x=3, 370 = 37/17 x
and so on.
Keep going till you find the constant you like.