The sum of two numbers is 69. The second is 9 more than 4 times the first. What are the two numbers?
would the equation i have be right
4x+y+9=69
4*15+0+9=69
60+9=69
couldn't it also be:
4x+y+9=69
4*14+4+9=69?
To solve the problem, we start by defining variables for the two unknown numbers. Let's say the first number is represented by "x," and the second number is represented by "y."
From the information given, we can translate the second statement into an equation: "The second number is 9 more than 4 times the first." This can be written as: y = 4x + 9.
Now, we know that the sum of the two numbers is 69, so we can write another equation: x + y = 69.
To find the values of x and y, we can solve these two equations simultaneously. Let's substitute the value of y from the first equation into the second equation:
x + (4x + 9) = 69
Combining similar terms:
5x + 9 = 69
Subtract 9 from both sides:
5x = 60
Divide both sides by 5:
x = 12
Now we can substitute the value of x back into the first equation to find y:
y = 4(12) + 9
y = 48 + 9
y = 57
Therefore, the two numbers are x = 12 and y = 57.
Regarding your specific equations:
1. 4x + y + 9 = 69
In this equation, you have correctly added 9 to the sum of 4x and y. However, you didn't arrive at the correct values for x and y.
2. 4x + y + 9 = 69
In this equation, you have multiplied 4 times x correctly and added 9 to it. However, you obtained different values for x and y compared to the correct solution.
Therefore, the correct equations to solve the problem are:
1. y = 4x + 9
2. x + y = 69