Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 4 - Review - Page 328: 33

Answer

Each egg costs 0.4USD while each strip of bacon cost 0.65USD.

Work Step by Step

Let $x$ be the cost of each egg and $y$ be the cost of each strip of bacon. Equation 1: $3x+4y=3.80$ Equation 2: $2x+3y=2.75$ We can solve for the value of $x$ and $y$ using addition method. Multiply equation 1 by $-2$ and equation 2 by $3$. Equation 1: $$[3x+4y=3.80]\cdot-2$$ $$-6x-8y=-7.6$$ Equation 2: $$[2x+3y=2.75]\cdot3$$ $$6x+9y=8.25$$ Add the resulting equations: $$-6x-8y=-7.6$$ $$+$$ $$6x+9y=8.25$$ $$=$$ $$y=0.65$$ Substitute this value of $y$ to equation 1: $$3x+4(0.65)=3.80$$ $$3x+2.6=3.80$$ Subtract $2.6$ from both sides: $$3x+2.6-2.6=3.80-2.6$$ $$3x=1.2$$ Divide both sides by $3$: $$\frac{3x}{3}=\frac{1.2}{3}$$ $$x=0.4$$ Use equation 2 to check: $$2(0.4)+3(0.65)=2.75$$ $$0.8+1.95=2.75$$ $$2.75=2.75$$
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