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dtan5457
 one year ago
August has four integers. When he adds them three at a time, the sums are 46,50,54 and 57. Compute the largest of the original four integers.
dtan5457
 one year ago
August has four integers. When he adds them three at a time, the sums are 46,50,54 and 57. Compute the largest of the original four integers.

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dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0So what I tried so far was setting up A+B+C=46 A+B+D=50 A+C+D=54 B+C+D=57 not sure how to solve this though

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0@Jhannybean @Nnesha @Loser66

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.0@agent0smith or even @zepdrix ? A little help here :)

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0I'm in a math research class so every question we get is supposed to be challenging lol

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0well you can solve them as simultaneous equations using matrices or just the hard slog of the elimination or substitution methods

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0i have never done matrices before

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0would substitution be a lot longer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this should be linear algebra u have 4 equations to solve 4 unknowns, have u tried ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what i'm not feeling okay about is this condition lol "Compute the largest of the original four integers"

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0i would rather just do this with substitution even if it took a while but im still a little stuck.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well good substitution is also away to solve i'll give you some hints

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2Using symmetry, you can solve it as follows.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2subtract (4) from (3) ab=3 subtract (3) from (2) bc=4 subtract (2) from (1) cd=4650=4 observe the three equations, a<b<c<d, so d is the largest of the 4. Now we know that adding all four equations together gives by symmetry 3(a+b+c+d)=207 a+b+c+d=69 substitute c=d4, b=d44=d8, a=d443=d11 we get 4d23=69 4d=92 d=23 voila

mathmate
 one year ago
Best ResponseYou've already chosen the best response.2got to go, talkk later!

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0finally solved it with subsitution and elimination, thanks anyways @mathmate

dtan5457
 one year ago
Best ResponseYou've already chosen the best response.0this is what i wrote on paper btw 4 integers=A,B,C,D "When he adds them three at a time" A+B+C=46 A+B+D=50 A+C+D=54 B+C+D=57 You can add them 3 at a time in 4 different ways, which is correctly shown in the system above. Step Two: Now, solving for just 1 of the 4 variables would easily lead the answers of the other three. For example, we will eliminate the variable A. 1. We can take the first two equations, and subtract them, to eliminate A. (We would get CD=4) 2. Next, we want to get another equation, without the variable A in it. We can use elimination for the 2nd and 3rd equation. We could get (BC=4) 3. Finally, we can use the last equation (also without the variable A). (B+C+D)=57 4. Now, we have the 3 equations: B+C+D=57. CD=4, BC=4 Beginning the elimination process, we can add the first 2 equations together and get B+2C=53. Now, we need either variable B or C in terms of the other, such as BC=4. We can say that B=4+C, which we will then plug back into 4+2C+2C=53. 4+4C=53. C=19. We have now solved one of the 4 variables. Step Three: Now that we know C=19, here comes the easy part, to solve for the other 3 variables, we simply plug into equation that contains the variable C. How about that equation CD=4 we received from the first elimination? (19)D=4, D=23. Now, we know that C=19 and D=23. We now have a even easier time solving for the last 2 variables. B+C+D=57, B+19+23=57, B=15 A+B+C=46, A+15+19=46, A=12 Step Four: Now, we have solved for all 4 variables. A=12, B=15, C=19, D=23. The question asks for the largest integer which is D=23, which is our final answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0actually u can add them in 4! different way but it won't be a problem as there is only one set solution
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