A store sells 2 1/4 pounds of mulch for every 1 1/2 pounds of gravel sold. The store sells 180 pounds of mulch and gravel combined. How many pounds of each item does the store sell?

Answer:The pounds of mulch the store sells are 108 and the pounds of gravel the store sells are 72.Step-by-step explanation:Letx -----> pounds of mulch the store sellsy ----> pounds of gravel the store sellswe know that[tex]x+y=180[/tex] -----> equation ARemember 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 Bsolve the system by substitutionsubstitute 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)thereforeThe pounds of mulch the store sells are 108 and the pounds of gravel the store sells are 72.