Let's begin by listing the first few multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 38, 40, 44. So, between 1 and 37 there are 9 such multiples: {4, 8, 12, 16, 20, 24, 28, 32, 36}. Note that 4 divided into 36 is 9.
Let's experiment by modifying the given problem a bit, for the purpose of discovering any pattern that may exist:
<span>How many multiples of 4 are there in {n; 37< n <101}? We could list and then count them: {40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100}; there are 16 such multiples in that particular interval. Try subtracting 40 from 100; we get 60. Dividing 60 by 4, we get 15, which is 1 less than 16. So it seems that if we subtract 40 from 1000 and divide the result by 4, and then add 1, we get the number of multiples of 4 between 37 and 1001:
1000
-40
-------
960
Dividing this by 4, we get 240. Adding 1, we get 241.
Finally, subtract 9 from 241: We get 232.
There are 232 multiples of 4 between 37 and 1001.
Can you think of a more straightforward method of determining this number? </span>
Answer: The variable t us the dependent variable because it affects the amount of money collected, m, each day.
<span><span>Answer/Work:
7.5 divided by 2.4 is
equivalent to 75 divided by 24,</span></span><span><span>
7.5/2.4 = 75/24 =3.125
calculating 3 decimal places.</span></span>
<span><span>Your answer is 3.125
</span></span>
Use elimination to find both values.
Subtract the second equation from the first equation
x + 15y = 40
- x + 10y = 30
————————
5y = 10
y = 2
Plug in the value for y into one of the equations. I’m going to put it in the second equation.
x + 10(2) = 30
x + 20 = 30
x = 10
x = 10
y = 2
