find three consecutive even intergers,

Question

such that five times the first, plus three times the third, is the same as seven times the second, plus ten.

then i have to

1. represent each interger

2.write an equation using the unknowns

3solve for three intergers

Answer 1

These are not so difficult if you think them through carefully.

 

Suppose the first even integer is x.

 

Then, the next even integer is 2 more than x or x + 2

 

Finally, the one after that is x + 4.

 

The integers are represented by x, x+2, and x+4

 

Now, five times the first means 5x

plus three times the third means 3 (x+4)

is

seven times the second means 7 (x+2)

 

so, 5x + 3 (x+4) = 7 (x+2) + 10               is the equation from the paragraph

5x + 3x + 12  = 7x + 14 + 10

8x + 12         =  7x + 24

x + 12           =   24

x                  =     12

x + 2 = 14

x+ 4  = 16

 

The three consecutive even integers are 12,14, and 16.

 

Check; 5 times the first means 60  (since 5*12=60)

plus 3 times the third means 48   (since 3*16=48)

60+48 = 108 for the left side of the equation

seven times the second means 98  (since 7*14=98)

98+10 = 108 for the right side of the equation

The equation balances perfectly, and it does check.

 

 

Answer 2

3 consecutive even integers will be:

 

n

n + 2

n + 4

 

Equation is:

 

5n + 3 (n + 4) = 7 (n + 2) + 10

 

remember to use the distributive property to work out the parentheses:

 

5n + 3n + 12 = 7n + 14 + 10

 

Combine terms:

 

8n + 12 = 7n + 24

 

Combine terms again, by subtracting 12 from both sides AND 7n from both sides, so

 

n = 12.  And if n = 12, you can then figure out what the next two even integers are.

 

Hope this helps. (And I hope I did it right!!)

 

Matt

Answer 3

Three consecutive even integers. So: 2, 4, 6, or 4, 6, 8, etc. Let X represent the first consecutive even integer we are looking for. Then [x+2] and [x+4] are the second and third integers we are looking for. Now that we have assigned variables to represent each integer, we need to translate the word problem into manageable formulas.

 

"Five times the first, plus three times the third, is the same as seven time the second, plus ten."

 

Translates to:

 

• 5x + 3[x+4] = 7[x+2] + 10
• 5x + 3x + 12 = 7x + 14 + 10
• 8x + 12 = 7x + 24
• x = 12

 

Thus, our three consecutive integers are 12, 14, and 16.

 

Now, as is ALWAYS a good idea, let's check our answer. 

 

"Five times the first, plus three times the third, is the same as seven time the second, plus ten."

 

"Five times 12, plus 3 times 16, is the same as 7 times 14 plus 10"

"60, plus 48, is the same as 98 + 10"

"108, is the same as 108"

 

Thus, we are correct :)