The difference between two numbers, p and q, where p > q is 19. Twice the greater number exceeds three times the smaller number by 21. Find the two numbers, p and q/
so, what do you know?
p = q+19
2p = 3q+21
Now just solve as usual for p and q
Let's use variables to represent the two numbers:
Let p be the greater number.
Let q be the smaller number.
According to the problem, we have two pieces of information:
1. The difference between p and q is 19: p - q = 19.
2. Twice the greater number exceeds three times the smaller number by 21: 2p = 3q + 21.
Now, we have a system of two equations with two variables. We can solve this system to find the values of p and q.
Let's solve the first equation for p:
p - q = 19
p = 19 + q
Substitute this expression for p into the second equation:
2p = 3q + 21
2(19 + q) = 3q + 21
38 + 2q = 3q + 21
Rearrange the equation to isolate q:
38 - 21 = 3q - 2q
17 = q
Now substitute the value of q back into the first equation to find p:
p = 19 + q
p = 19 + 17
p = 36
Therefore, the two numbers are q = 17 and p = 36.
To find the two numbers, p and q, we can set up a system of equations based on the given information.
Let's define p as the greater number and q as the smaller number.
From the given information, we know that p - q = 19. This equation represents the difference between the two numbers.
We are also given that twice the greater number (2p) exceeds three times the smaller number (3q) by 21. Mathematically, this can be written as:
2p = 3q + 21
Now we have a system of equations:
p - q = 19
2p = 3q + 21
To solve this system, we can use the method of substitution or elimination. Let's solve by substitution:
From the first equation, we can isolate p by adding q to both sides:
p = q + 19
Now substitute this value of p into the second equation:
2(q + 19) = 3q + 21
Simplify the equation:
2q + 38 = 3q + 21
Subtract 2q from both sides:
38 = q + 21
Subtract 21 from both sides:
17 = q
Now we have found the value of q, which is 17. To find the value of p, substitute this value back into the first equation:
p - 17 = 19
Add 17 to both sides:
p = 19 + 17
p = 36
Therefore, the two numbers are p = 36 and q = 17.