Question

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

Answer 1

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.

⇒
`43.50x+65.50y = 745.10`

Then the system of equation we get;

`x+y =13` .....[1]

`43.50x+65.50y = 745.10` .....[2]

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

`43.50x+43.50y = 565.50` .....[3]

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

`43.50x+65.50y-43.50x-43.50y = 745.10-565.50`

Combine like terms;

`22y = 179.60`

Divide both sides by 22 we get;

`y = 8.1636 \approx 8`

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 =
`8 \cdot 65.95=\$527.60`

⇒He spent $527.60 on large cabinets.