The sum of two consecutive integers is at least 185. what is the smaller of the two integers? enter your answer in the box.

Mathematics

2 answers:

Zinaida [17]3 years ago

5 0

Answer: 92

Trust me I did this already and got an A 100% hope this helps.

Have a great day!!!

ss7ja [257]3 years ago

4 0

Let us assume the first integer to be = x
Then
The second integer will be = x + 1
The sum of the two consecutive integers =185
Then
x + x + 1 = 185
2x + 1 = 185
2x = 184
x = 92
From the above deduction, we can easily conclude that the smallest of the two integers is 92. I hope that the answer has helped you.

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Katyanochek1 [597]

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2 years ago

Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 32 ft long. She wants to leave a uniform strip of floor aroun

Rainbow [258]

Answer:

The rug should be 15 ft wide and 28 ft long.

Step-by-step explanation:

I have attached a figure that represents the situation.

The the rug is $l$ by $h$ , the width of the strip of floor is $w$ .

We are told that Cynthia can only afford 420 square feet of carpeting; therefore, it must be that

$l*h=420$ (this says the area of the rug must be 420 square feet)

From the figure we see that

$l= 32-2w$

$h=19-2w$

Therefore,

$l*h=420\\\\(32-2w)(19-2w)=420$

We expand this equation and get:

$4w^2-102w+608=420\\\\4w^2-102w+188=0$

using the quadratic equation we get two solutions:

$w=2\\w=23.5$

since the second solution, namely $w=23.5$ , is larger than one of the dimensions of the room (is greater than 19 ft) it cannot be the width of the strip; therefore, we take $w=2$ to be our solution.