Answer:
The cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]
Explanation:
Let x and y represent the cost of a cupcake and cookie respectively.
Given that;
Five cupcakes and two cookies cost $19.75.
[tex]5x+2y=19.75-------1[/tex]
Two cupcakes and four cookies cost $17.50.
[tex]2x+4y=17.50-------2[/tex]
Let's solve the simultaneous equation by elimination;
multiply equation 1 by 2;
[tex]10x+4y=39.50-------3[/tex]
subtract equation 2 from equation 3;
[tex]\begin{gathered} 10x-2x+4y-4y=39.50-17.50 \\ 8x=22 \\ \text{divide both sides by 8;} \\ \frac{8x}{8}=\frac{22}{8} \\ x=2.75 \end{gathered}[/tex]
since we have the value of x, let substitute into equation 1 to get y;
[tex]\begin{gathered} 5x+2y=19.75 \\ 5(2.75)+2y=19.75 \\ 13.75+2y=19.75 \\ 2y=19.75-13.75 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3.00 \end{gathered}[/tex]
Therefore, the cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]
