175 bags of mulch sold for $520 . Two types of mulch sold : hardwood for $3.50 per bag and pine bark for $2.75 per bag. How many bags of each were sold

Question

Need an equation and answer

Answer 1

X = number of hardwood bags

Y = number of pine bark

 

X + Y = 175

 

3.50X + 2.75Y = 520

 

 

 

Solves the first equation for Y

Y = 175 - X

 

Multiplies the second equation by 100 

to clear the decimals:

 

350X + 275Y = 52000

 

Substitutes the first equation into the second:

350X + 275 ( 175 - X) = 52000

 

350X + 48125 - 275X = 52000

 

75X = 3875

 

 X = 51 and 2/3

 

Y = 175 -    51 and 2/3 = 123 and 1/3

 

CHECK:   3.50 * (51 and 2/3) + 2.75 * (123 and 1/3) = 520