A girl earns $6.00 an hour when she works Monday through Friday and $9.00 an hour on Saturday. Last week, her salary was $273 for 42 hours of work. How many hours did she work on Saturday?
first, represent unknowns with variables:
let x = number of hours she worked for monday-friday
let y = number of hours she worked for saturday
set up equation according to conditions given:
(1) x + y = 42
(2) 6x + 9y = 273
there are many ways to solve for this,, if we use substitution method,,
choose an equation (in this case, equation (1)), then express one of the variables in terms of the other,, thus we express x in terms of y:
x + y = 42
x = 42 - y
now we substitute this to equation (2):
6x + 9y = 273
6(42-y) + 9y = 273
now you solve for y.
To find the number of hours the girl worked on Saturday, we can set up an equation based on the given information.
Let's assume that the girl worked x hours on Saturday.
From Monday to Friday, she earns $6.00 per hour. So, the total earnings from Monday to Friday can be calculated as 6 * 5 = $<<6*5=30.00>>30.00.
On Saturday, she earns $9.00 per hour. So, the earnings for Saturday can be calculated as 9 * x = $9x.
The total earnings for the week is given as $273.
Combining the earnings from Monday to Friday with the earnings from Saturday, we can set up the equation:
30.00 + 9x = 273
To solve for x, we can simplify the equation:
9x = 273 - 30.00
9x = 243
Now, divide both sides of the equation by 9:
x = 27
Therefore, the girl worked 27 hours on Saturday.