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Source Sited: https://www.theodysseyonline.com/

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Source Sited: http://slideplayer.com/slide/4773902/

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The basic facts:
Lundy and his sister wanted to save money for the upcoming vacation.
- They both have $20 in their bank account and they receive $10 per week for allowance.
- What if their cousin is going on the same trip but she has $60 in her account and she receives $15 per week for allowance.

The question:
- How many weeks will it take for Lundy and his sister to save up the same amount of money as their cousin?

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Source Sited: https://www.desmos.com/calculator

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To solve a system of two equations, we simply set each equation equal to each other.

However, Given that there are two separate equations for Lundy and her sister, it is necessary to combine those equations into one equation.

Equation for Lundy:
y=10x + 20
Equation for Lundy's sister:
y= 10x + 20

Equation for BOTH Lundy and her sister:
y = 20x + 40

Equation for the cousin:
y = 15x + 60

Now that there are only two equations, simply set them equal to one another and solve for the missing variable.
y = 20x + 40
y = 15x + 60

20x + 40 = 15x + 60
5x + 40 = 60
5x = 20
x = 4

This answer tells us that it will take Lundy and her sister 4 weeks to earn the same amount of money as their cousin.

The total amount of money for Lundy and her sister will be $120.

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Equation for a linear expression: y=mx+b

Equation for Lundy and his sister
y=10x+20

The equation is like this because of what it says in the problem. The 20 is the "b" because its the start of the problem and the 10 is the "m" because that's how much money they are going to make each week.

Equation for their cousin
y=15x+60

The equation is like this because of what it says in the problem.The 60 is the "b" because its at the start of the problem and the 15 is the "m" because that's how much money they are going to make each week.