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Chapter 11: Problem 9

$$11 x+14 y=30 \text { and } 3 x+4 y=12$$ $$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ x+y & (x+y)^{-2} \end{array}$$ a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
The answer is (a). Quantity A is greater.

Step by step solution

01

Solve for the unknowns in the equations

Solving the system of equations \[11x + 14y = 30\] and \[3x + 4y = 12\] using substitution or elimination method gives the values of \(x = 2\) and \(y = 1\).
02

Substitute the values into Quantity A

Quantity A is expressed as \(x + y\). Substituting the solved values gives \(2+1\), which simplifies to \(3\).
03

Substitute the values into Quantity B

Quantity B is expressed as \((x + y)^{-2}\). Substituting the values \(2\) and \(1\) into the expression gives \((3)^{-2} = 1/9\).
04

Compare Quantity A and Quantity B

Comparing the results of Quantity A and Quantity B, \(3\) and \(1/9\) respectively, gives the insight that Quantity A is greater than Quantity B.

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Most popular questions from this chapter

If \(x=3 a\) and \(y=9 b,\) then all of the following are equal to \(2(x+y)\) EXCEPT a. \(3(2 a+6 b)\) b. \(6(a+3 b)\) c. \(24\left(\frac{1}{4} a+\frac{3}{4} b\right)\) d. \(\frac{1}{3}(18 a+54 b)\) e. \(12\left(\frac{1}{2} a+\frac{3}{4} b\right)\)

A merchant sells three different sizes of canned tomatoes. A large can costs the same as 5 medium cans or 7 small cans. If a customer purchases an equal number of small and large cans of tomatoes for the same amount of money needed to buy 200 medium cans, how many small cans does she purchase? a. 35 b. 45 c. 72 d. 199 e. 208

If \(A=2 x-(y-2 c)\) and \(B=(2 x-y)-2 c,\) then \(A-B=\) a. \(-2 y\) b. \(-4 c\) c. \(-0\) d. \(-2 y\) e. \(-4 c\)

$$\begin{array}{cc}\text { Quantity } \mathbf{A} & \text { Quantity } \mathbf{B} \\ \frac{2^{-4}}{4^{-2}} & \frac{\sqrt{64}}{-2^{3}} \end{array}$$ a. Quantity A is greater b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

If \(a\) is multiplied by 3 and the result is 4 less than 6 times \(b,\) what is the value of \(a-2 b ?\) a. -12 b. \(-\frac{4}{3}\) c. \(-\frac{3}{4}\) d. \(\frac{4}{3}\) e. 12
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