More Systems of equations?

Question

Solve.

1.) X+Y+Z=20000

2.) .05X+.07Y+.10Z=1390

3.) X=Z+3000

PLEASE SHOW ALL WORK!!

Answer 1

X + Y + Z = 20000

.05X + .07Y + .10Z = 1390

X = Z + 3000

Solve the first equation for Y.

X + Y + Z = 20000

Y = 20000 - Z - X  

Call this equation *1*

Substitute *1* and the third equation into the second equation and solve for Z.

.05X + .07Y + .10Z = 1390

.05(Z + 3000) + .07(20000 - Z - X) + .1Z = 1390

.05(Z + 3000) + .07(20000 - Z - (Z + 3000)) + .1Z = 1390

.05Z + 150 + .07(20000 - Z - (Z + 3000)) + .1Z = 1390

.05Z + 150 + 1400 - .07Z - .07(Z + 3000) + .1Z = 1390

.05Z + 150 + 1400 - .07Z - .07Z - 210 + .1Z = 1390

.05Z + 150 + 1400 - .14Z - 210 + .1Z = 1390

.05Z + 1400 - .14Z - 60 + .1Z = 1390

.05Z + 1400 - .04Z - 60 = 1390

.05Z + 1340 - .04Z = 1390

.01Z + 1340  = 1390

.01Z = 50

Z = 5000

Substitute this into the third equation and solve for X.

X = Z + 3000

X = 5000 + 3000

X = 8000

Substitute this into *1* and solve for Y.

Y = 20000 - Z - X  

Y = 20000 - 5000 - 8000

Y = 7000

Answer:  X = 8000, Y = 7000, Z = 5000

Hope this helps you!