Given that x:y = 3:4 and y:z = 5:8, find the value of 2y3x−y+2x

We need to write the expression in terms of one variable. We are given that xy=34 so x=(3/4)y and that zx=58 so y=(58)z. It follows that x in terms of z is x=34((58)z)=(1532)z Hence, we can write the expression in terms of z: 2y3x−y+2z=2(58)z3(1532)z−58z+2=54z4532z−58z+2z=54z4532z−54z⋅44+2z3232=54z4532z−(2032)z+6432z=54z8932z=548932=543289=4089

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High School
Algebra
Algebra I
Exponents and radicals

sodni3

Answered question

2021-05-04

Given that x:y = 3:4 and y:z = 5:8, find the value of

2 \frac{y}{3 x - y + 2 x}

Answer & Explanation

averes8

Skilled2021-05-05Added 92 answers

We need to write the expression in terms of one variable. We are given that $\frac{x}{y} = \frac{3}{4}$ so x=(3/4)y and that $\frac{z}{x} = \frac{5}{8}$ so $y = (\frac{5}{8}) z$ . It follows that x in terms of z is $x = \frac{3}{4} ((\frac{5}{8}) z) = (\frac{15}{32}) z$
Hence, we can write the expression in terms of z:
$\frac{2 y}{3 x - y + 2 z} = 2 \frac{(\frac{5}{8}) z}{3 (\frac{15}{32}) z} - \frac{5}{8} z + 2 = \frac{\frac{5}{4} z}{\frac{45}{32} z} - \frac{5}{8} z + 2 z = \frac{\frac{5}{4} z}{\frac{45}{32} z} - \frac{5}{4} z \cdot \frac{4}{4} + 2 z \frac{32}{32} =$ $\frac{\frac{5}{4} z}{\frac{45}{32} z - (\frac{20}{32}) z + \frac{64}{32} z} = \frac{\frac{5}{4} z}{\frac{89}{32} z} = \frac{\frac{5}{4}}{\frac{89}{32}} = \frac{5}{4} \frac{32}{89} = \frac{40}{89}$

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