Question

4. 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. Write and solve a system of equations to find the number of small cabinets and large cabinets he purchased. Determine if each statement is True or False. A. He purchased 5 small cabinets. B. He purchased 7 large cabinets. O Yes O No C. He spent $527.60 on large cabinets. O Yes O No

Answer 1

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.

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

`(6595x)/(100) + (4350y)/(100) = (74510)/(100)`

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

`y =(11225)/(2245)`

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