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.
