yan gets allowance money every day. On Monday he gets 5 cents. On Tuesday he gets 12 cents. On Wednesday he gets 19 cents. On Thursday he gets 30 cents. On Friday he gets 35 cents. How much will he get on Saturday? How much will he have by the 12th day? The 16th day? When will he be able to buy a new bicycle?
I'm just guessing here...
Saturday: 42 cents
12th day: 90 cents
16th day: 120 cents
And I don't know how much the bicycle costs
Hope this helps! Sorry if not. :(
To find out how much Yan will get on Saturday, we need to identify the pattern in his allowance.
If we look at the given allowances for each day, we can notice that the amounts are increasing by 7 cents each day. So, on Saturday (the 6th day), he will get 35 + 7 = 42 cents.
To calculate how much he will have by the 12th day, we need to add up the allowances for each day from Monday to Saturday. Since the sequence follows an arithmetic progression, we can use the formula:
Sn = (n/2) * (2a + (n-1)d)
Where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
For Yan's allowance, the first term (a) is 5 cents and the common difference (d) is 7 cents.
By substituting these values into the formula, we get:
S12 = (12/2) * (2*5 + (12-1)*7)
= 6 * (10 + 11 * 7)
= 6 * (10 + 77)
= 6 * 87
= 522 cents
Therefore, Yan will have 522 cents after the 12th day.
Similarly, to find out how much he will have by the 16th day, we substitute n = 16 into the formula:
S16 = (16/2) * (2*5 + (16-1)*7)
= 8 * (10 + 15 * 7)
= 8 * (10 + 105)
= 8 * 115
= 920 cents
So, Yan will have 920 cents after the 16th day.
Now, to determine when Yan will be able to buy a new bicycle, we need to know the cost of the bicycle.
If we have that information, we can divide the cost of the bicycle by Yan's daily allowance (which is increasing by 7 cents each day) to determine the number of days it will take for him to save up enough.
Please provide the cost of the bicycle, and I can help you calculate when Yan will be able to buy it.