Let:
x = Number of candy bars
y = Number of lollipops
a = cost of a candy bar
b = cost of a lollipop
Ms. Watson spent $11.90 to buy a total of 20 candy bars, so:
[tex]x+y=20[/tex]and:
[tex]\begin{gathered} ax+by=11.90 \\ 1.40x+0.25y=11.90 \end{gathered}[/tex]Let:
[tex]\begin{gathered} x+y=20_{\text{ }}(1) \\ 1.40x+0.25y=11.90_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for y:
[tex]y=20-x_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 1.40x+0.25(20-x)=11.90 \\ 1.40x+5-0.25x=11.90 \\ 1.15x=11.90-5 \\ 1.15x=6.9 \\ x=\frac{6.9}{1.15} \\ x=6 \end{gathered}[/tex]Replace the value of x into (3):
[tex]\begin{gathered} y=20-6 \\ y=14 \end{gathered}[/tex]Ms watson bought 6 candy bars and 14 lollipops
