Respuesta :
Answer:
The number of big cabinets are 8 and the number of small cabinets are 5 .
True , Asif purchased 5 small cabinets.
False , No Asif purchased 7 large cabinets.
True ,Asif spent $527.60 on large cabinets.
Step-by-step explanation:
Let us assume that the number of big cabinets are x .
Let us assume that the number of small cabinets be y .
As given
Asif spent $745.10 on 13 new file cabinets for his office.
Small file cabinets cost $43.50 and large file cabinets cost $65.95.
Equation becomes
x + y = 13
65.95x + 43.50y = 745.10
Simplify the above
[tex]\frac{6595x}{100} + \frac{4350y}{100} = \frac{74510}{100}[/tex]
6595x + 4350y = 74510
Two equations are
x + y = 13
6595x + 4350y = 74510
Multiply x + y = 13 by 6595 and subtracted from 6595x + 4350y = 74510 .
6595x - 6595x + 4350y - 6595y = 74510 - 85735
-2245y = -11225
2245y = 11225
[tex]y =\frac{11225}{2245}[/tex]
y = 5
Putting the value of y in the equation
x + 5 = 13
x = 13 - 5
x = 8
Therefore the number of big cabinets are 8 and the number of small cabinets are 5 .
First Part
True , Asif purchased 5 small cabinets.
Second Part
False , No Asif purchased 7 large cabinets.
As Asif purchased 8 big cabinets .
Third Part
True ,Asif spent $527.60 on large cabinets.
As there are 8 large cabinets and large file cabinets cost $65.95.
Total cost of big cabinets = 8 × 65.95
= $ 527.60
