SOLUTION: AL, ART AND ANNA WORK IN A STORE. LAST WEEK, ART WORKED 6HRS LESS THAN TWICE AL'S HRS. ANNA WORKED 10HRS MORE THAN ART. ALTOGETHER, THEY WORKED 103HRS. HOW MANY HRS DID ART WORK LA

Algebra ->  Human-and-algebraic-language -> SOLUTION: AL, ART AND ANNA WORK IN A STORE. LAST WEEK, ART WORKED 6HRS LESS THAN TWICE AL'S HRS. ANNA WORKED 10HRS MORE THAN ART. ALTOGETHER, THEY WORKED 103HRS. HOW MANY HRS DID ART WORK LA      Log On


   



Question 689316: AL, ART AND ANNA WORK IN A STORE. LAST WEEK, ART WORKED 6HRS LESS THAN TWICE AL'S HRS. ANNA WORKED 10HRS MORE THAN ART. ALTOGETHER, THEY WORKED 103HRS. HOW MANY HRS DID ART WORK LAST WEEK?
Answer by MathLover1(20850) About Me  (Show Source):
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ART WORKED 6HRS LESS THAN TWICE AL'S HRS. ANNA WORKED 10HRS MORE THAN ART. ALTOGETHER, THEY WORKED 103HRS.
let’s Anna’s work hours be x, Al’s work hours be y, and Art’s work hours be z
given:
they all together worked:
x%2By%2Bz=103h.........1
Art worked 6h less than twice Al’s hours:
z=2y-6h................2
Anna worked 10h more than Art:
x=z%2B10h............3
now, solve this system:
x%2By%2Bz=103h.........1
z=2y-6h................2
x=z%2B10h............3
________________________
take first
x%2By%2Bz=103h.........1...substitute x from eq. 3
z%2B10h%2By%2Bz=103h.....solve for y
2z%2By=103h-10h
y=93h-2z..........................1a.....go to eq. 2 and substitute y
z=2%2893h-2z%29-6h................2....solve for z
z=186h-4z-6h
z%2B4z=180h
5z=180h
z=180h%2F5
highlight%28z=36h%29..go to eq. 1a and substitute z



y=93h-2%2A36h
y=93h-72h
highlight%28y=21h%29
now, go to any eq. above, plug in values for y and z and find x

x%2By%2Bz=103h.........1
x%2B21h%2B36h=103h
x%2B57h=103h
x=103h-57h
highlight%28x=46h%29
so, Art worked 36h hours last week