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You and your sister have been saving and decide to buy a Playstation 5 together. You need $500 to
buy the Playstation. Together you have $850 saved up. Since you have more money, you contribute
50% of your savings and your sister contributes 75% of hers toward the $500 cost. How much do each
of you have saved individually?

a. Write a system of equations in standard form to model this situation


b. Solve this system of equations using eliminations

Answer :

According to the information given, we have that:

a) The system of equations is given by: x + y = 850, 0.5x + 0.75y = 500.

b) You has saved $550 and your sister has saved $300.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

  • Variable x: The amount you have saved up.
  • Variable y: The amount your sister has saved up.

Item a:

Together you have $850 saved up, hence:

x + y = 850.

You contribute 50% of your savings and your sister contributes 75% of hers toward the $500 cost, hence:

0.5x + 0.75y = 500.

Item b:

From the first equation, we have that:

x = 850 - y

Replacing on the second:

0.5(850 - y) + 0.75y = 500

0.25y = 75

y = 75/0.25

y = 300

x = 850 - y = 550.

You has saved $550 and your sister has saved $300.

More can be learned about a system of equations at https://brainly.com/question/24342899

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