On October 10, the Miller family received 31 pieces of mail, consisting of magazines, bills, letters, and ads. If they received the same number of magazines as letters, three more bills than letters, and five more ads than bills, how many magazines did they receive?
Well, it seems like the Miller family's mailbox was quite the hot spot on October 10! Let's solve this mystery, shall we?
Let's assume the number of letters received by the Miller family is "x." Since they received the same number of magazines as letters, we can say the number of magazines is also "x."
Now, we know that the number of bills is three more than the number of letters. So, the number of bills would be "x + 3."
According to the information given, the number of ads is five more than the number of bills. Therefore, the number of ads can be expressed as "(x + 3) + 5," which simplifies to "x + 8."
Adding up the total number of pieces of mail, we have:
x + x + (x + 3) + (x + 8) = 31
Simplifying that equation, we get:
4x + 11 = 31
Subtracting 11 from both sides, we have:
4x = 20
Dividing both sides by 4, we find:
x = 5
So, the Miller family received 5 magazines. I hope this solves the puzzling mail mystery for you!
Let's use a step-by-step approach to solve this problem.
Step 1: Let's denote the number of magazines as 'm', the number of bills as 'b', the number of letters as 'l', and the number of ads as 'a'.
Step 2: We know that the Miller family received a total of 31 pieces of mail, so we can write an equation: m + b + l + a = 31.
Step 3: We also know that they received the same number of magazines as letters, so we can write another equation: m = l.
Step 4: We are given that they received three more bills than letters, so we can write the following equation: b = l + 3.
Step 5: We are also given that they received five more ads than bills, so we can write the following equation: a = b + 5.
Step 6: Now we can substitute equations (3) and (4) into equations (2) and (5) to express 'm' in terms of 'l' and solve for 'l'.
Substituting equation (3) into equation (2): m = l becomes l = l, which is trivially true.
Substituting equation (4) into equation (5): a = b + 5 becomes a = l + 3 + 5, which simplifies to a = l + 8.
Step 7: Substituting the expressions for 'm' and 'a' in terms of 'l' into the first equation (1): m + b + l + a = 31 becomes l + b + l + l + 8 = 31, which simplifies to 3l + b + 8 = 31.
Step 8: Rearranging the equation, we have 3l + b = 31 - 8, which is 3l + b = 23.
Step 9: Since 'b' is expressed in terms of 'l' in equation (3), we can substitute b = l + 3 into equation (8): 3l + (l + 3) = 23.
Step 10: Simplifying the equation, we have 4l + 3 = 23.
Step 11: Subtracting 3 from both sides, we get 4l = 20.
Step 12: Dividing both sides by 4, we find that l = 5.
Step 13: Now that we know the value of 'l', we can use equation (3) to find the value of 'b': b = l + 3 = 5 + 3 = 8.
Step 14: Finally, we can use equation (2) to find the value of 'm': m = l = 5.
So, the Miller family received 5 magazines.
To determine how many magazines the Miller family received, let's break down the information provided:
1. The number of magazines is equal to the number of letters.
2. There were three more bills than letters.
3. There were five more ads than bills.
Let's start by assigning variables to the unknowns:
Let M be the number of magazines.
Let L be the number of letters.
Let B be the number of bills.
Let A be the number of ads.
From the given information, we can set up a system of equations:
1. The number of magazines is equal to the number of letters: M = L. (Equation 1)
2. There were three more bills than letters: B = L + 3. (Equation 2)
3. There were five more ads than bills: A = B + 5. (Equation 3)
Now, let's substitute equations 1 and 2 into equation 3 to eliminate variables:
A = (L + 3) + 5
A = L + 8. (Equation 4)
We also know that the total number of pieces of mail received is 31:
M + L + B + A = 31. (Equation 5)
Substituting equations 1, 2, 4, and 5 into equation 5, we can solve for the number of magazines, M:
M + L + (L + 3) + (L + 8) = 31
4L + 12 = 31
4L = 31 - 12
4L = 19
L = 19 / 4
L ≈ 4.75.
Since L represents the number of letters, it cannot be a decimal value. However, we know from equation 2 that the number of bills is three more than the number of letters, so it must be a whole number. Therefore, we can conclude that there is an error in the given information or the question.
Without a clear value for the number of letters (and consequently, the number of magazines), we cannot accurately determine the number of magazines the Miller family received.
m = magazines and letters
m+3 = bills
m+3+5 = m+8 = ads
so, m + m + m+3 + m+8 = 31