smaller ---- x
larger ----- x+21
2x + (1/2)(x+21) = 38
each term times 2
4x + (x+21) = 76
should be easy to solve for x
larger ----- x+21
2x + (1/2)(x+21) = 38
each term times 2
4x + (x+21) = 76
should be easy to solve for x
We are given that the difference between the two numbers is 21, which can be written as the equation:
y - x = 21
Next, we are told that twice the smaller number, which is 2x, added to one-half of the larger number, which is (1/2)y, equals 38. This can be expressed as the equation:
2x + (1/2)y = 38
Now we have a system of two equations with two variables. We can solve this system using either substitution or elimination method.
Let's use the substitution method:
1. Rearrange the first equation to solve for y:
y = x + 21
2. Substitute this expression for y in the second equation:
2x + (1/2)(x + 21) = 38
3. Simplify the equation:
2x + (1/2)x + (1/2)(21) = 38
2x + (1/2)x + 10.5 = 38
4x + x + 21 = 76 (multiplying both sides by 2 to clear the fraction)
5x = 55
x = 11
4. Substitute the value of x back into the first equation to solve for y:
y = x + 21
y = 11 + 21
y = 32
Therefore, the smaller number is 11 and the larger number is 32.