Awarding more pointsrobin has $24.50 and her brother wayne has $68.50. her brother is paying her $2.75 each day to with his chores. when will they have the same amount of money? how much money will they have?
a) write a system of equations to solve this problem. state what your variables represent.
b) solve and explain what your answers mean.

a) y = 2.75x + 24.50 and y = 68.50 - 2.75x; where x is the number of days and y is the amount of money

b) (8, 46.5). 8 is the number of days and 46.50 is the amount of money.

Step-by-step explanation:

Question a)

Write equations to represent the amount of money each of the siblings have. When a number has a variable attached to it, it changes based on the variable's value. A number without a variable is generally the initial amount, of the starting money they have.

let "y" be the total amount of money and "x" be the days Robins helps Wayne

Since Robin is paid when she does chores, she gains money:

y = 2.75x + 24.50

Since Wayne pays Robin his money, he loses money:

y = 68.50 - 2.75x

Question b)

We can solve using elimination. This is the simpler method because they already have a common variable and coefficient: 2.75x

Since the 2.75x in the equations have opposite signs (negative and positive), we add the equations to cancel it out.

.       y = 2.75x + 24.50        Robin

+      y = -2.75x + 68.50       Wayne

.     2y = 0x + 93         0x means that the variable is cancelled out

.     2y = 93

.  2y/2 = 93/2               Divide both sides by 2 to find "y"

.       y = 46.5

Find "x" by substituting y for 46.5 into any of the equations.

y = 2.75x + 24.50

46.5 = 2.75x + 24.50

Isolate "x" by cancelling numbers in reverse BEDMAS order

46.5 - 24.50 = 2.75x + 24.50 - 24.50      Subtract 24.50 to isolate x

22 = 2.75x

22/2.75 = 2.75x/2.75      Divide both sides by 2.75 to isolate x

8 = x

x = 8          Writing the variable on the left side is standard formatting

The solution to the system is (8, 46.5). This means that Robin and Wayne will have the amount amount of money in 8 days. The amount of money they will each have in 8 days is $46.50.