Jerry started doing sit ups every day. The first day he did 15 sit ups. Every day after that he did 2 more sit ups than he had done the previous day.
Today Jerry did to 33 sit ups. Write an equation that could be solved to find the number of days Jerry has been doing sit ups, not counting the first day.
S = 2d + 13 , where S is the number of situps, d is the number of days, d≥1 , d is an integer.
check:
if d = 1, (first day) , S = 15
if d = 2 (2nd day) , S = 17
yup that works
so if S = 33
33 = 2d + 13
2d = 20
d = 10
We could arrange the equation:
2d + 13 = S
2d = S - 13
d = (S - 13)/2
I really don't know what you mean by "not counting the first day". Why not ?
Let's assume that the number of days Jerry has been doing sit ups, not counting the first day, is represented by "d".
On the first day, Jerry did 15 sit ups.
From the second day onwards, Jerry did 2 more sit ups than he did the previous day.
Therefore, the number of sit ups Jerry did on the second day is (15 + 2) = 17.
The number of sit ups Jerry did on the third day is (17 + 2) = 19.
The number of sit ups Jerry did on the fourth day is (19 + 2) = 21.
We can see that the number of sit ups Jerry did on any given day can be represented by the equation:
Sit ups = (15 + 2d)
We are given that Jerry did 33 sit ups today, so we can set up the equation:
33 = (15 + 2d)
To solve the equation for "d", we can subtract 15 from both sides:
33 - 15 = 15 + 2d - 15
18 = 2d
Finally, we can divide both sides by 2 to solve for "d":
18/2 = 2d/2
9 = d
Therefore, the number of days Jerry has been doing sit ups, not counting the first day, is 9.
To find the number of days Jerry has been doing sit-ups, we need to determine how many times he increased the number of sit-ups by 2.
Let's assume the number of days Jerry has been doing sit-ups is represented by "d".
On the first day, Jerry did 15 sit-ups. We need to exclude this day from our count.
Starting from the second day, he increased the number of sit-ups by 2 each day.
So, on the second day, Jerry did 15 + 2 = 17 sit-ups.
On the third day, he did 15 + 2 + 2 = 19 sit-ups.
And so on.
In general, the number of sit-ups Jerry did on any given day (excluding the first day) can be represented by the equation:
Sit-ups = 15 + 2*(d - 1)
Where:
Sit-ups: The number of sit-ups Jerry did on a specific day (excluding the first day).
"d": The number of days Jerry has been doing sit-ups (excluding the first day).
According to the question, today Jerry did 33 sit-ups, so we can use this information to solve the equation:
33 = 15 + 2*(d - 1)
Now we can solve this equation to find the value of "d".