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Question 5 (Multiple Choice Worth 2 Points)
(Systems of Linear Equations MC)

Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account can be represented by the equation [tex]\( y = 10x + 20 \)[/tex]. Sibling B's savings can be represented by the equation [tex]\( y = 5x + 50 \)[/tex].

Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?

A. 2.5 weeks
B. 5 weeks
C. 15 weeks
D. 75 weeks



Answer :

GinnyAnswer
To determine after how many weeks the savings accounts of sibling A and sibling B will have the same amount of money, we can set up and solve a system of linear equations based on the information given.

1. Define the Variables and Equations:
- Let [tex]\( x \)[/tex] represent the number of weeks.
- Let [tex]\( y \)[/tex] represent the amount of money in the savings accounts.

2. Savings Equations:
- Sibling A's savings can be represented by the equation [tex]\( y = 10x \)[/tex].
- Sibling B's savings can be represented by the equation [tex]\( y = 5x + 50 \)[/tex].

3. Set the Equations Equal to Find the Intersection Point:
[tex]\[ 10x = 5x + 50 \][/tex]

4. Solve the Equation:
[tex]\[ 10x = 5x + 50 \][/tex]
[tex]\[ 10x - 5x = 50 \][/tex]
[tex]\[ 5x = 50 \][/tex]
[tex]\[ x = \frac{50}{5} \][/tex]
[tex]\[ x = 10 \][/tex]

The two siblings' savings accounts will have the same amount of money after 10 weeks. Hence, the correct answer is not among the given options. This appears to be an error in the provided multiple-choice options. However, based on the data provided and the steps taken above, the correct answer should be:

10 weeks.

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