Question

The sum of 2 CONSECUTIVE integers is greater than 73.
- Write an inequality to describe the situation.
- Solve the inequality.
- Find the pair of integers with the least sum.

Answer 1

help please??

Answer 2

let's pick one number, ok?

Answer 3

so say one integer is a, then the next consecutive integer is a + 1

their sum is a + a + 1

and this has to be greater than 73

\[a + a + 1 > 73\]
\[2a + 1 > 73\]

move the 1 to the other side and divide by two

\[a > 36\]

Answer 4

Yes! I got the same answer but what are the 2 numbers?

Answer 5

37 and the next consecutive 38 :)

Answer 6

ohhhhhhh , okay. may you help me on another one please?

Answer 7

sure

Answer 8

okay thanks. The length of a rectangle is 2 inches more than its width, and its perimeter is no more than 68 inches
- write an inequality to describe the situation.
- solve the inequality.
-what are the greatest possible dimensions of the rectangle.

Answer 9

okay so firstly declare variables. lets do length = l, width = w perimiter = p (pretty easy)
now use the relationships.

l is 2 inches more than w, so l = w + 2.
perimiter is no more than 68, so \[p \le 68\]

now we want to get rid of p from the inequality because we need our answer in terms of the dimensions... l and w.

p = 2l + 2w.

replace this p with the one in the inequality.

\[2l + 2w \le 68\]

we already have l in terms of w, so lets replace l

\[2(w + 2) + w \le 68\]
\[2w + 2 \le 68\]
\[w \le 22\]

Answer 10

no sorry im not sure

Answer 11

okay..well thanks anyways.