Answer:
The pounds of mulch the store sells are 108 and the pounds of gravel the store sells are 72.
Step-by-step explanation:
Let
x -----> pounds of mulch the store sells
y ----> pounds of gravel the store sells
we know that
[tex]x+y=180[/tex] -----> equation A
Remember that
[tex]2\frac{1}{4}\ lb=\frac{2*4+1}{4}=\frac{9}{4}\ lb[/tex]
[tex]1\frac{1}{2}\ lb=\frac{1*2+1}{2}=\frac{3}{2}\ lb[/tex]
so
[tex]\frac{x}{y}=\frac{(9/4)}{(3/2)}[/tex]
[tex]\frac{x}{y}=\frac{3}{2}[/tex]
[tex]x=\frac{3}{2}y[/tex] -----> equation B
solve the system by substitution
substitute equation B in equation A
[tex]\frac{3}{2}y+y=180[/tex]
solve for y
[tex]\frac{5}{2}y=180[/tex]
[tex]y=180(2)/5\\y=72[/tex]
Find the value of x
[tex]x=\frac{3}{2}(72)=108[/tex]
The solution is the ordered pair (108,72)
therefore
The pounds of mulch the store sells are 108 and the pounds of gravel the store sells are 72.
