Answer:
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.
⇒[tex]43.50x+65.50y = 745.10[/tex]
Then the system of equation we get;
[tex]x+y =13[/tex] .....[1]
[tex]43.50x+65.50y = 745.10[/tex] .....[2]
Multiply equation [1] by 43.50 both sides we get;
[tex]43.50x+43.50y = 565.50[/tex] .....[3]
Subtract equation [3] from equation [2] to eliminate x we get;
[tex]43.50x+65.50y-43.50x-43.50y = 745.10-565.50[/tex]
Combine like terms;
[tex]22y = 179.60[/tex]
Divide both sides by 22 we get;
[tex]y = 8.1636 \approx 8[/tex]
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 = [tex]8 \cdot 65.95=\$527.60[/tex]
⇒He spent $527.60 on large cabinets.
