QuestionCourse: 24/FA College Al... My Courses Pearson MyLab and Mast... Homework, and Quizzes Do Homework - Section 7... Fatima Alhindawy 11/26/24 6:46 AM 7.1 Homework 7.1.89 Part 1 of 3 crontratim Gnom: 650 \% 65 of 10 moints Pomis: 0 of 1 Sav
The total spending on Black Friday during 2011 and 2012 was $\$ 1919$ million. From 2011 to 2012, spending increased by $\$ 225$ million. (a) Write a system of equations whose solution represents the Black Friday spending in each of these years. Let $x$ be the amount spent in 2012 and $y$ be the amount spent in 2011. (b) Solve the system. (c) Interpret the solution. (a) Choose the correct answer below. A. $\begin{array}{l} x+y=1919 \\ y=x+225 \end{array}$ $\qquad$ c. $\begin{array}{l} x+y=225 \\ y=x+1919 \end{array}$ B. $\begin{array}{l} x+y=1919 \\ x=y+225 \end{array}$ $\qquad$ D. $\begin{array}{l} x+y=225 \\ x=y+1919 \end{array}$

Studdy Solution

STEP 1

1. The total spending on Black Friday during 2011 and 2012 was $1919$ million.
2. From 2011 to 2012, spending increased by $225$ million.
3. Let $x$ be the amount spent in 2012.
4. Let $y$ be the amount spent in 2011.
5. We need to write a system of equations and solve it.

STEP 2

1. Write the system of equations based on the problem description.
2. Solve the system of equations.
3. Interpret the solution.

STEP 3

Write the system of equations based on the problem description.
From the problem, we have two key pieces of information: - The total spending for both years is $1919$ million. - The spending in 2012 is $225$ million more than in 2011.
This gives us the equations: $x + y = 1919$ $x = y + 225$
The correct answer is: B. $\begin{array}{l} x+y=1919 \\ x=y+225 \end{array}$

STEP 4

Solve the system of equations.
Substitute the second equation into the first equation: $(y + 225) + y = 1919$
Simplify: $2y + 225 = 1919$
Subtract 225 from both sides: $2y = 1694$
Divide by 2: $y = 847$
Now substitute back to find $x$ : $x = y + 225$ $x = 847 + 225$ $x = 1072$

STEP 5

Interpret the solution.
The solution to the system of equations is: - The amount spent in 2011 ( $y$ ) was $847$ million. - The amount spent in 2012 ( $x$ ) was $1072$ million.
This means that in 2011, $847$ million was spent, and in 2012, $1072$ million was spent, which aligns with the given increase of $225$ million from 2011 to 2012.

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