Question

Find two consecutive even numbers such that the difference of one-half the larger number and two-fifths the smaller number is equal to five.



38 and 40

40 and 42

42 and 44

Answer 1

im having trouble working it out can i get a good explaniaition

Answer 2

if one even number is \(n\), the next consecutive even number will be \(n+2\).

one-half the larger number = \(\frac{n+2}{2}\)
two-fifths the smaller number = \(\frac{2}{5}n\)
difference of those two is equal to five:

\[\frac{n+2}{2}-\frac{2}{5}n = 5\]

Multiply everything by 2*5 to get rid of the fractions, then solve for \(n\). \(n,n+2\) will be the answer.

Answer 3

that really doesnt help

Answer 4

both numbers are even, so you know the bigger one divided by 2 will give an integer number.

2/5 the smaller one will be an integer only if it is divisible by 5... meaning we can look for the answer that has the smaller number which is divisible by 5... that is not really solving the problem, but it does get you the answer.

Answer 5

do i dive by 2/5 or

Answer 6

@dirtydan667 how doesn't it help? what do you get if you multiply each term in that equation by 10?

Answer 7

divide*

Answer 8

dan, do you understand how wh got the equation?
and do you know how to solve it ?

Answer 9

i like to do it the simple waqy i figures it out im X the number by 1/2 or 2/5 not dividing

Answer 10

i figured*



i*

Answer 11

multiplying by ½ is the same as dividing by 2... don't be confused by how it is written... it means the exact same thing.

to solve an equation with fractions, write this in your notebook:

CLEAR the DENOMINATOR

Answer 12

Clear the denominator means multiply the equation by any number that is in the denominator. You can do it in steps, or all at once.

To do it in steps, notice 2 is in the denominator. Multiply the equation by 2
(that means *all* terms, *both* sides)
and then simplify

then see that 5 is in the denominator... multiply the equation by 5
can you do that ?

Answer 13

let me solve it the way i do it ill be right back brb

Answer 14

k im back i got b

Answer 15

??

Answer 16

\[\frac{n+2}{2}-\frac{2}{5}n = 5\]Multiply everything by 2*5:
\[\cancel{2}*5*\frac{(n+2)}{\cancel{2}} - 2*\cancel{5}*\frac{2}{\cancel{5}}n =2*5*5\]\[5(n+2) - 4n = 50\]\[5n+10-4n=50\]\[n=50-10=40\]\[n+2=40+2=42\]

Answer 17

If you know how to solve them, you shouldn't need us to check your work for you. If you think 40 and 42 are the answer, try them out and make sure they satisfy the problem:

40 is the smaller number
42 is the larger number
1/2 the larger number - 2/5 the smaller number = 5
(1/2)*42 - (2/5)*40 = 5
does that simplify to a true statement?

Answer 18

thanks for the help

Answer 19

You should be able to decide yourself with certainty whether you are correct for this problem.

Answer 20

checking the choices is a good strategy.
But you really should try to learn how to solve these problems. The answer is not as important as solving the problem using math.

Answer 21

yes, that is good. But it is even better to be able to write down the equation, and then solve the equation.

Answer 22

nvm i had a self relization

Answer 23

an ephinay of sourts

Answer 24

Being able to write down the equation means you understand the question (a lot better) than someone who can't. It you can't figure out these *trivial* (compared to the real world) problems, you will be (relatively) clueless. Think of math as *simple* thinking. That is what you are really learning.