How do you solve #\frac { 13} { 4} ( \frac { 31} { 8} r + 1) = \frac { 5423} { 56}#?

1 Answer
Sep 8, 2017

#r=7.43#

Explanation:

#13/4(31/8r+1)=5423/56#

As always, equations of one unknown can be approached by expanding, and then isolating the unknown one side of the equation.

#13/4*31/8r+13/4=5423/56#
#(13*31)/(4*8)r+13/4=5423/56#

Now we subtract #13/4# from both sides to get isolate the unknown's term. (The unknown's (r's) coefficient is also simplified.)

#403/32r+13/4-13/4=5423/56-13/4#
#403/32r=5423/56-13/4#

Then taking common denominator and simplifying the ride side of the equation.

#403/32r=5423/56-(13*14)/(4*14)# (since 4*14=56)
#403/32r=(5423-(13*14))/56#
#403/32r=(5423-182)/56# (since 13*14=182)
#403/32r=5241/56#

Now as of a final step we have to multiply both sides by 32 and divide by 403, to isolate the unknown.

#403/32r*32/403=5241/56*32/403#
#r=5241/56*32/403=(167712)/(22568)=7.43#
(since #5241*32=167712# and #56*403=22568#)

I hope that this helps. :)