please help

Question

a slice of pie with a scoop of ice cream has 640 calories. the calories in the pie alone are 100 more than the ice cream alone. how many calories are in each food?

Answer 1

Let's assign variables to the information in the problem...

 

p=calories in pie alone

s=calories in scoop of ice cream alone

s+100=p....Eq1, calories in pie alone, given info

p+s=640....Eq2, calories, pie and scoop, given info

 

Let's substitute Eq1 into Eq2...

          p+s=640...Eq2

(s+100)+s=640...substitute for "p", solve for "s"

     2s+100=640...combine like terms

             2s=540...subtract 100, both sides

          ∴  s=270...divide both sides by 2

 

Substitute "s=270" into Eq1, solve for "p"...

    s+100=p.......Eq1

270+100=p......substitute for "s", solve for "p"

        370=p.......simplify

        ∴ p=370...rewrite

 

Let's check our solution...

    s+100=p........Eq1

270+100=370...substitute for "s,p"

         370=370...true, √check

 

        p+s=640.....Eq2

270+370=640....substitute for"s,p"

         640=640....true, √check

 

Always check your solution and work!  Our solution is correct and satisfies problem statement requirements.  

 

So...

370 calories in pie alone,

270 calories in scoop of ice cream alone.