Four distinct integers a, b, c, and d have the property that when added in pairs, the sums 10, 18, 19, 20, 21, and 29 are obtained. What are the four integers in increasing order?

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The solution is very easy.

Of the 4 integers a, b, c, d, there are 6 possible sums:

a + b

a + c

a + d

b + c

b + d

c + d

Assume

a + b = 16

a + c = 19

a + d = 20

b + c = 21

b + d = 22

c + d = 25

Subtract the first equation from the second to get

c - b = 3

Now, add this to the fourth equation to get

2c = 24, so

c = 12

The rest follows easily from this:

Since c=12, a + c = 19 implies a = 7

Since a=7, a + b = 16 implies b = 9

Since a=7, a + d = 20 implies d = 13

Since b=9, b + c = 21 implies c = 12

Therefore the answer will be 7, 9, 12, and 13

Done and done!

the correct answer is 828.07

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

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