Respuesta :
Given:
The charge for a small office = $55.
The charge for a large office = $ 85.
The total number of offices = 14.
The total amount = $ 920.
Required:
We need to find a number of small offices and large offices.
Explanation:
Let x be the number of the small office and y be the number of the large office.
The equation of the total number of offices.
[tex]x+y=14[/tex][tex]x=14-y[/tex]The equation of the total amount.
[tex]55x+85y=920[/tex]Substitute x =14-y in the equation.
[tex]55(14-y)+85y=920[/tex][tex]55\times14-55y+85y=920[/tex][tex]770+30y=920[/tex]Subtract 770 from both sides of the equation.
[tex]770+30y-770=920-770[/tex][tex]30y=150[/tex]Divide both sides by 30.
[tex]\frac{30y}{30}=\frac{150}{30}[/tex][tex]y=5[/tex][tex]Substitute\text{ y=5 in the equation x=14-y.}[/tex][tex]x=14-5[/tex][tex]x=9[/tex]Final answer:
The equations are
[tex]x+y=14[/tex][tex]55x+85y=920[/tex]The number of small offices are 9.
The number of large offices are 5.
