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

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

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 = 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