the sum of two numbers is 20. one number is 1 less than twice the other. find the numbers
n and 2n-1
n + 2n - 1 = 20
3 n = 21
Mark has $3.55 in nickels and dimes. If he has a total of 42 coins, how many of each kind of coins does he have?
To find the two numbers, let's assume that one number is represented by x and the other number is represented by y.
According to the given information:
1) The sum of the two numbers is 20, so we can write the equation: x + y = 20.
2) One number is 1 less than twice the other, which can be written as: x = 2y - 1.
Now, we have a system of two equations with two variables. We can solve this system to find the values of x and y using either substitution or elimination method.
Let's use the substitution method:
1) Start with the first equation: x + y = 20.
2) Solve the second equation for x: x = 2y - 1.
3) Substitute the value of x in the first equation: (2y - 1) + y = 20.
4) Simplify the equation: 3y - 1 = 20.
5) Add 1 to both sides of the equation: 3y = 21.
6) Divide both sides of the equation by 3: y = 7.
Now, substitute the value of y into the second equation: x = 2(7) - 1.
Evaluate: x = 14 - 1.
Simplify: x = 13.
Therefore, the two numbers are x = 13 and y = 7.