Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

From 1970 to 1990 the average per person annual consumption of whole milk declined at a constant rate from 101 to 41 quarts per year. During the same period, the average annual consumption of low fat milk increased at a constant rate from 25 to 60 quarts per year. What was the average annual per person consumption when the consumption of whole milk and low fat milk was the same? Choose 1 answer: (A) 53 quarts (B) 55 quarts (c) 57 quarts (D) 59 quarts

From \(1970\) to \(1990\) the average per person annual consumption of whole milk declined at a constant rate from \(101\) to \(41\) quarts per year. During the same period, the average annual consumption of low fat milk increased at a constant rate from \(25\) to \(60\) quarts per year. What was the average annual per person consumption when the consumption of whole milk and low fat milk was the same?\newlineChoose 11 answer:\newline(A) \(53\) quarts\newline(B) \(55\) quarts\newline(C) \(57\) quarts\newline(D) \(59\) quarts

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Interpret parts of quadratic expressions: word problemsright chevron icon

Full solution

Q. From \(1970\) to \(1990\) the average per person annual consumption of whole milk declined at a constant rate from \(101\) to \(41\) quarts per year. During the same period, the average annual consumption of low fat milk increased at a constant rate from \(25\) to \(60\) quarts per year. What was the average annual per person consumption when the consumption of whole milk and low fat milk was the same?\newlineChoose 11 answer:\newline(A) \(53\) quarts\newline(B) \(55\) quarts\newline(C) \(57\) quarts\newline(D) \(59\) quarts
  1. Determine rate of decline for whole milk: Determine the rate of decline for whole milk consumption.\newlineThe decline in whole milk consumption over 2020 years (from 19701970 to 19901990) is from 101101 quarts to 4141 quarts. This is a total decline of 101−41=60101 - 41 = 60 quarts over 2020 years.\newlineRate of decline for whole milk=Total declineNumber of years=60 quarts20 years=3 quarts per year\text{Rate of decline for whole milk} = \frac{\text{Total decline}}{\text{Number of years}} = \frac{60 \text{ quarts}}{20 \text{ years}} = 3 \text{ quarts per year}
  2. Determine rate of increase for low fat milk: Determine the rate of increase for low fat milk consumption.\newlineThe increase in low fat milk consumption over the same 2020 years is from 2525 quarts to 6060 quarts. This is a total increase of 60−25=3560 - 25 = 35 quarts over 2020 years.\newlineRate of increase for low fat milk=Total increaseNumber of years=35 quarts20 years=1.75quarts per year\text{Rate of increase for low fat milk} = \frac{\text{Total increase}}{\text{Number of years}} = \frac{35 \text{ quarts}}{20 \text{ years}} = 1.75 \text{quarts per year}
  3. Set up equation for equal milk consumption: Set up an equation to find the year when the consumption of whole milk and low fat milk was the same.\newlineLet xx be the number of years after 19701970 when the consumptions are equal.\newlineStarting with 101101 quarts for whole milk and subtracting 33 quarts per year, we get: 101−3x101 - 3x.\newlineStarting with 2525 quarts for low fat milk and adding 1.751.75 quarts per year, we get: 25+1.75x25 + 1.75x.\newlineSet the two expressions equal to each other: 101−3x=25+1.75x101 - 3x = 25 + 1.75x
  4. Solve equation for x: Solve the equation for x.\newlineCombine like terms: 101−25=3x+1.75x101 - 25 = 3x + 1.75x\newline76=4.75x76 = 4.75x\newlineDivide both sides by 4.754.75 to solve for xx: x=764.75x = \frac{76}{4.75}\newlinex≈16x \approx 16
  5. Calculate average annual consumption: Calculate the average annual per person consumption when the consumptions are equal.\newlineSubstitute xx back into either the whole milk or low fat milk equation: 101−3(16)101 - 3(16) or 25+1.75(16)25 + 1.75(16).\newlineUsing the whole milk equation: 101−3(16)=101−48=53101 - 3(16) = 101 - 48 = 53 quarts.\newlineUsing the low fat milk equation: 25+1.75(16)=25+28=5325 + 1.75(16) = 25 + 28 = 53 quarts.\newlineBoth equations should give the same result, which is the point where the consumptions are equal.

More problems from Interpret parts of quadratic expressions: word problems

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 7 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 5 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 4 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 5 months ago

View all (97)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant