3 story problems

peachgal · #1 $Old$ November 9th, 2008, 05:50 PM

1. A change machine contains nickels , dimes, and quarters. there are 75 coins in the machine, and the value of the coins is $7.25. If there are 5 times as many nickels as dimes, find the number of coins of each type in the machine.

2. The sum of the digits of a 3 digit number is 18. Three times the tens digit minus 5 times the units (ones) digit is 17. If 4 times the units digit is added to twice the hundreds digit, the result is 22. Find the 3 digit number.

3. A rectangular box is twice as long as it is wide and twice as wide as it is high. The sum of its length, width, and height is 35 in. What are the dimensions of the box?

and this short problem : find x and y (matrices)

[ 0 2 ] [ x 4 ] = [ -2 6 ]
3 0 -1 3y 12 12 i dont know how to make then line up

Soroban · #2 $Old$ November 9th, 2008, 08:10 PM

Hello, peachgal!

Here's the set-up for #2 . . .

Let . $\begin{Bmatrix}H &=& \text{hundreds digit} \\ T &=& \text{tens digit} \\ U &=& \text{units digit} \end{Bmatrix}$

Quote:

2. The sum of the digits of a-3 digit number is 18: . . . . . . . . ${\color{blue}H + T + U \:=\:18}$
Three times the tens digit minus 5 times the units digit is 17:. . ${\color{blue}3T + 5U \:=\:17}$
4 times the units digit plus twice the hundreds digit is 22: . . . . ${\color{blue}4U + 2H \:=\:22}$

Find the 3-digit number.

Now solve the system of equations . . .

muks · #3 $Old$ November 10th, 2008, 07:28 AM

3. A rectangular box is twice as long as it is wide and twice as wide as it is high. The sum of its length, width, and height is 35 in. What are the dimensions of the box?

Let the height be x.
Then width= 2x
Length = 4x
Sum=7x
7x= 35
x=5
The height is 5 in, width is 10 in. and length is 20 in.