Please help! Math word problem in description below! Thank you!

Question

Cassie opened a cafe near Central Park. A small cup of coffee sells for $3.00 and a medium cup sells for $4.00. On the first day 158 cups were sold, and Cassie made 570. How many cups of each size were sold?

Answer 1

Let's assume

 

s= no. of small cup of coffee

m= no. of medium cup of coffee

 

money earn from small cup of coffee = $3s

money earn from medium  cup of coffee =$4m

 

On the first day 158 cups were sold,

 

so

 

s+m=158     ________________equation 1

 

and Cassie made 570

 

3s+4m=570  _______________equation 2

 

solve equation 1 and equation 2 simultaneously

 

s+m=158

s=158 -m

substitute value of s in equation 2

 

3(158-m) +4m = 570 

 

474 -3m + 4m =570

 

m+474 = 570

 

m=96

 

substitute value of m in equation 1

 

s+m= 158

 

s+96=158

 

s= 62

 

Number of small cup of coffee sold= 62

number of medium cup of coffee sold = 96

 

Answer 2

Let s=small cup and m=medium cup

 

two equations, one for number of cups

s + m = 158 cups      

 

and one for dollars

3s + 4m = 570

 

use substitution to solve

 s+m=158     so    s=158-m

 

3s + 4m = 570

3(158-m) + 4m = 570

474 - 3m + 4m = 570

474 + m = 570

-474         -474

        m = 96         they sold 96 medium cups

 

now substitute the number of mediums to find the number of smalls using the first equation

s = 158 - 96

s = 62               they sold 62 small cups