Answer:
Step-by-step 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]10x-2x+4y-4y=39.50-8x=22[/tex]
[tex]8x=22[/tex]
divide both sides by 8
[tex]\frac{8x}{8} =\frac{22}{8} \\x=2.75[/tex]
Since we have the value of x, let substitute into equation 1 to get y;
[tex]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[/tex]
therefore , the cost of cupcakes and cookies are;
[tex]cupcakes= 2.75\\cookies= 3.00[/tex]
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