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. 1. he purchased 5 small cabinets. true or false 2. he purchased 7 large cabinets. true or false 3. he spent $527.60 on large cabinets. true or false

Let x represents the number of small cabinets and y represents the number of large cabinets purchased.

As per the statement:

Asif spent $745.10 on 13 new file cabinets for his office. S

⇒x+y =13

It is also given that: Small file cabinets cost $43.50 and large file cabinets cost $65.95.

⇒

Then the system of equation we get;

                         .....[1]

         .....[2]

Multiply equation [1] by 43.50 both sides we get;

           .....[3]

Subtract equation [3] from equation [2] to eliminate x we get;

Combine like terms;

Divide both sides by 22 we get;

Substitute the value of y = 8 in [1] we get;

x + 8 = 13

Subtract 8 from both sides we get;

x = 5

Therefore, number of small cabinets is 5 and number of large cabinets is 8

1.

True, because

He purchased 5 small cabinets.

2.

False, as

he purchase 8 large cabinets not 7 large cabinets

3

True.

Each Large file cabinets cost $65.95.

On 8 large cabinet =

⇒He spent $527.60 on large cabinets.