The cost of bagel is $0.8; and the cost of muffin is $1.25
Let the cost of a bagel be $x and the cost of a muffin be $y
From the question
Ten bagels and four muffins cost $13
That is,
10x + 4y = $13 ---------- (1)
Also,
Five bagels and eight muffins cost $14
That is,
5x + 8y = $14 ----------- (2)
Now, we will solve the two equations simultaneously
From equation (1)
10x + 4y = 13
Make y the subject of the equation
[tex]4y = 13 -10x[/tex]
[tex]y = \frac{13-10x}{4}[/tex] ------------ (3)
Substitute this into equation (2)
[tex]5x + 8y = $14[/tex]
[tex]5x + 8(\frac{13-10x)}{4}) = $14[/tex]
This gives
[tex]5x + 2(13-10x) =14[/tex]
[tex]5x + 26-20x=14[/tex]
Collect like terms
[tex]5x - 20x = 14 - 26[/tex]
[tex]-15x =-12[/tex]
Now, divide both sides by -15
[tex]\frac{-15x}{-15} =\frac{-12}{-15}[/tex]
[tex]x = 0.8[/tex]
Substitute the value of x into equation (3) to get y
[tex]y = \frac{13-10x}{4}[/tex]
[tex]y = \frac{13-10(0.8)}{4}[/tex]
[tex]y = \frac{13-8}{4}[/tex]
[tex]y =\frac{5}{4}[/tex]
[tex]y = 1.25[/tex]
∴ x = 0.8 and y = 1.25
Hence, the cost of bagel is $0.8; and the cost of muffin is $1.25
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