Answer:
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.
