The sum of three numbers is 23. The first number is equal to twice the second number minus 7. The third number is equal to one more than the sum of the first and second numbers. What is the First Number?
just write the facts in symbols.
x+y+z = 23
x = 2y-7
z = 1+(x+y)
Now just solve for x.
2nd number ---- x
1st number = 2x-7
3rd = x + 2x-7 + 1 = 3x - 6
x + 2x-7 + 3x - 6 = 23
carry on
A change machine contains nickels,dimes, and quarters. There are 75 coins in the machine, and the value of the coins is $7.25. There are 5 times as many nickels as dimes. How many quarters are in the machine?
To find the first number, we need to translate the given information into equations and solve for the first number.
Let's call the second number "x".
According to the given information:
The first number = 2x - 7.
The third number = (first number + second number) + 1 = (2x - 7 + x) + 1 = 3x - 6.
Now we can set up the equation using the sum of the three numbers:
First number + second number + third number = 23.
Substituting in the expressions we found:
(2x - 7) + x + (3x - 6) = 23.
Simplifying:
6x - 13 = 23.
Adding 13 to both sides:
6x = 36.
Dividing by 6:
x = 6.
Therefore, the second number (x) is 6.
Now, we can find the first number:
First number = 2x - 7 = 2(6) - 7 = 12 - 7 = 5.
So, the first number is 5.