3. Mrs.Galicia bought 3 tacos and 2 sodas and paid $9.75. The next day she went back and bought 5 tacos and 1 soda and paid $12.75. (a) Write and solve a system of equations that model the problem. Show all your work. (b) How much was one soda? (c) How much was one taco?

(a) System of equations: [tex]\bold{3m + 2n = 9.75}[/tex] and [tex]\bold{5m + n = 12.75}[/tex] (b) One soda costs [tex]\bold{\$1.5}[/tex](c) One taco costs [tex]\bold{\$2.25}[/tex]SOLUTION:Given, Mrs. Galicia bought 3 tacos and 2 sodas and paid [tex]\$9.75[/tex].  The next day she went back and bought 5 tacos and 1 soda and paid [tex]\$12.75[/tex].  Let the cost of 1 tacos be m, and cost of 1 soda be n.Now, We have to find  (a) System of equations:  3 tacos and 2 sodas cost [tex]\$ 9.75 \rightarrow 3 \times m+2 \times n=\$ 9.75 \rightarrow 3 m+2 n=9.75 \rightarrow(1)[/tex]5 tacos and 1 soda cost [tex]\$ 12.75 \rightarrow 5 \times m+1 \times n=\$ 12.75 \rightarrow 5 m+n=12.75 \rightarrow(2)[/tex]System of equations are  [tex]3m + 2n = 9.75[/tex]  [tex]5m + n = 12.75[/tex]Now, [tex](2) \rightarrow n=12.75-5 m[/tex]So, substitute n in (1)[tex]\begin{array}{l}{3 m+2(12.75-5 m)=9.75} \\\\ {3 m+25.5-10 m=9.75} \\\\ {10 m-3 m=25.5-9.75} \\\\ {7 m=15.75}\end{array}[/tex][tex]\begin{array}{l}{m=2.25, \text { then, } n=12.75-5 \times 2.25} \\\\ {n=12.75-11.25=1.5} \\\\ {\text {SQ, } m=2.25 \text { and } n=1.5}\end{array}[/tex](b) cost of one soda [tex]\$ 1.5[/tex](c) cost of one taco [tex]\$ 2.25[/tex]