Suppose that y varies jointly with w and x and inversely with z and y=360 when w=8, x=25 and z=5. How do you write the equation that models the relationship. Then find y when w=4, x=4 and z=3?

Question

Eva Adamson · Accepted Answer

#y =48# under the given conditions
(see below for the modelling)

If #color(red)y# varies jointly with #color(blue)w# and #color(green)x# and inversely with #color(magenta)z# then #color(white)("XXX")(color(red)y * color(magenta)z)/(color(blue)w *color(green)x) = color(brown)k# for some constant #color(brown)k# GIven #color(white)("XXX")color(red)(y=360)# #color(white)("XXX")color(blue)(w=8)# #color(white)("XXX")color(green)(x=25)# #color(white)("XXX")color(magenta)(z=5)# #color(brown)k=(color(red)(360) * color(magenta)(5))/(color(blue)(8) * color(green)(25))# #color(white)("XX")=(cancel(360)^45 * cancel(5))/(cancel(8) * cancel(25)_5# #color(white)("XX")= color(brown)9# So when #color(white)("XXX")color(blue)(w=4)# #color(white)("XXX")color(green)(x=4)# and #color(white)("XXX")color(magenta)(z=3)# #color(white)("XXX")(color(red)y * color(magenta)3)/(color(blue)4 * color(green)4) = color(brown)9# #color(white)("XXX")color(red)y = (color(brown)9 * color(blue)4 * color(green)4)/color(magenta)3 = 48#

Julia Adams · Answer

undefined The equation that models the relationship is $ y = \frac{{kwx}}{{z}} $. By substituting the given values for $ y $, $ w $, $ x $, and $ z $ into the equation $ y = \frac{{kwx}}{{z}} $, we can solve for $ k $. Then, we can use the value of $ k $ to find $ y $ when $ w = 4 $, $ x = 4 $, and $ z = 3 $.

$ 360 = \frac{{8 \times 25 \times k}}{{5}} $

$ k = \frac{{360 \times 5}}{{8 \times 25}} $

$ k = 9 $

Now that we have $ k = 9 $, we can use it to find $ y $ when $ w = 4 $, $ x = 4 $, and $ z = 3 $:

$ y = \frac{{4 \times 4 \times 9}}{{3}} = 48 $