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4 years ago

The sum of two numbers is 64 . the smaller number is 14 less than the larger number. what are the numbers?

Mathematics

1 answer:

Katyanochek1 [597]4 years ago

5 0

..2x+14=64
x=25
...x+y=64
25+y=64
y=39
x is the smallest,y is the largest

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The denominator of a fraction is 4 more than the numerator if both are decreased by 3 the simplified result is 6/7 find original

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Answer:

The denominator of a fraction is 4 more than the numerator. The original fraction is $\frac{27}{31}$

Solution:

Given that

Denominator of fraction is 4 more than the numerator.

Let’s say numerator of fraction be represented by variable x.

So denominator of a faction as it is four more that numerator will be x + 4

Also given if both decreased by three than simplified result is $\frac{6}{7}$

$=>\frac{(x-3)}{((x+4)-3)}=\frac{6}{7}$

Solving above equation for x

=> 7(x – 3 ) = 6 ( x + 1 )

=> 7x – 21 = 6x + 6

=> 7x – 6x = 6 + 21

=> x = 27

Numerator of fraction = x = 27

Denominator of fraction = x + 4 = 27 + 4 = 31

$\text {required fraction}=\frac{\text {numerator}}{\text {denominator}}$

$= \frac{27}{31}$

Hence the original fraction is $\frac{27}{31}$

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Zach is a shoe salesman, and he works on commission. This week, there is a special incentive to sell shoes and boots by a certai

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Answer:

Zach earns $10 and for the pair of boots Zach earns $15

Step-by-step explanation:

Let be x the number of pairs of shoes

Let be y the number of pairs of boots

Then we can establish the following system of equations with the data of the statement:

$5x + 9y = 185 \\7x + 9y = 205$

We subtract the second equation from the first equation to eliminate the variable y and solve for x, just like this:

$7x+9y-5x-9y=205-185\\2x=20\\x=\frac{20}{2}\\x=10$

For y replacing in the first equation the value of x and solving for y:

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So for the pair of shoes Zach earns $10 and for the pair of boots Zach earns $15

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angle HJK

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