Let's set up a system of equations:
It's important to define variables:
Let #w="washer"#
Let #d="dryer"#
"A washer and a dryer cost $823 combined" is in English, but in Math terms it would be:
#w+color(blue)(d)=823#
"The washer costs 73 more than the dryer" is simply:
#color(purple)(w)=color(red)(d+73)#
Let's solve the first equation in terms of #d#:
#color(purple)(w)+color(blue)(d)=823#
#color(red)(d+73)+color(blue)(d)=823# #color(blue)(" Substitute and replace ")color(purple)(w)#
#color(red)(2d+73)=823# #color(blue)(" Combine like terms; d+d=2d")#
#color(red)(2d)=750# #color(blue)(" 823 - 73=750")#
#color(red)(d=375)# #color(blue)(750/2 = 375)#
Now that we have #d#, let's plug it back into the other (second) equation that we haven't used yet to solve for #w#:
#color(purple)(w)=color(red)(d+73)#
#color(purple)(w)=color(red)(375+73)# #color(blue)(" Substitute 375 for "d)#
#color(purple)(w=448)# #color(blue)(" Add")#
Now we have the prices for the washer and dryer:
#color(purple)(w=$448)#
#color(red)(d=$375)#
Let's double check:
#w+color(blue)(d)=823#
#color(purple)(448)+color(red)(375)=823# #color(blue)(" Plug in the values we found for w and d")#
#823=823# #color(blue)(" True")#
Now the second equation:
#color(purple)(w)=color(red)(d)+73#
#color(purple)(448)=color(red)(375)+73# #color(blue)(" Plug in the values we found for w and d")#
#823=823# #color(blue)(" True")#
Now that we've double checked, we can be 100% certain that our answers are correct.
