Concept: An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Let x,x+2,x+4 be the least, middle and greatest integer respectively.

According to the question,

15< x+x+2+x+4< 21

(3x+6)/2> 15 and (3x+6)/2< 21

30< 3x+6 3x+6> 42

24<3x 3x<36

8<x x>12

x=10

x+2=12

x+4=14

Hence, The even integers are 10,12 and 14.

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4 0

2 years ago

A jar contains sugar. The jar and the sugar have a total weight of 850 g. Anna uses 2/3 of the sugar. The jar and the sugar now

maria [59]

Answer:

$J = 370g$

Step-by-step explanation:

Given

Represent the weight of the Jar with J and the sugar with S

Initially, we have:

$J + S = 850g$

After 2/3 of sugar is removed we have:

$J + S -\frac{2}{3}S= 530g$

Required

Determine the weight of the jar

$J + S = 850g$ --- (1)

$J + S -\frac{2}{3}S= 530g$ --- (2)

Simplify (2)

$J + S -\frac{2S}{3}= 530g$

Take LCM

$J + \frac{3S - 2S}{3}= 530g$

$J + \frac{S}{3}= 530g$

Make S the subject in (1)

$J + S = 850g$

$S = 850g - J$

Substitute 850g - J for S in $J + \frac{S}{3}= 530g$

$J + \frac{850g - J}{3}= 530g$

Multiply through by 3

$3 * J + 3*\frac{850g - J}{3}= 530g * 3$

$3J + 850g - J= 1590g$

Collect Like Terms

$3J - J= 1590g-850g$

$2J= 740g$

Make J the subject

$J = \frac{1}{2} * 740g$

$J = 370g$

<em>The jar weighs 370g</em>

5 0

3 years ago

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