SOLUTION: Q2. The difference of two numbers is 4. The sum of thrice the larger number and four times the smaller number is 61. Find the number. Q2. A block of wood is 75cm ×50cm×40cm. How m

Algebra ->  Volume -> SOLUTION: Q2. The difference of two numbers is 4. The sum of thrice the larger number and four times the smaller number is 61. Find the number. Q2. A block of wood is 75cm ×50cm×40cm. How m      Log On


   

Question 1027785: Q2. The difference of two numbers is 4. The sum of thrice the larger number and four times the smaller number is 61. Find the number.
Q2. A block of wood is 75cm ×50cm×40cm. How many cube of side 0.1m can be carved out of it?
Answer by Cromlix(4381) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,
The difference of two numbers is 4.
x - y = 4.......(1)
The sum of thrice the larger number
and four times the smaller number is 61.
3x + 4y = 61.....(2)
Simultaneous equations:
x - y = 4.......(1)
3x + 4y = 61....(2)
Multiply Eq(1) by 4
4x - 4y = 16....(1)
3x + 4y = 61....(2)
Add Eq(1) + Eq(2)
7x = 77
x = 11
Substitute x = 11 into Eq(2)
3x + 4y = 61.....(2)
3(11) + 4y = 61
33 + 4y = 61
4y = 61 - 33
4y = 28
y = 7
Two numbers: 11 and 7
.......................
Convert sizes from centimeters
to meters:
0.75m x 0.5m x 0.4m
= 0.15m^3
Volume of a cube of side 0.1m
length x breadth x height
= (0.1m)^3 = 1 x 10^-3m^3
0.15m^3/1 x 10^-3m^3
= 150 cubes.
Hope this helps :-)