SOLUTION: A hardware company has two locations with a total of 26 employees. If four times the number of employees at the larger location is six less than seven times the number of employees
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Question 1152245: A hardware company has two locations with a total of 26 employees. If four times the number of employees at the larger location is six less than seven times the number of employees at the smaller​ location, how many employees are at each​ location? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! x = number of employees at the larger location.
y = number of employees at the smaller location.
the two equations that need to be solved simultaneously are:
x + y = 26
4x = 7y - 6
rearrange the second equation so that the variables are on the left and the constants are on the right, and leave the first equation as is to get:
x + y = 26
4x - 7y = -6
multiply both sides of the first equation by 4 and leave the second equation as is to get:
4x + 4y = 104
4x - 7y = -6
subtract the second equation from the first to get:
11y = 110
solve for y to get:
y = 110 / 11 = 10
solve for x to get x = 16
replace original equations with x = 16 and y = 10 to get:
x + y = 26 becomes 16 + 10 = 26 which becomes 26 = 26.
4x = 7y - 6 becomes 4 * 16 = 7 * 10 - 6 which becomes 64 = 64.
this confirms the values for x and y are correct.
your solution is that there are 16 employees at the larger location and 10 employees at the smaller location.
