Mildred sold magazine subscriptions with three prices: $22, $18, and $15. She sold 2 fewer of the $22 subscriptions than of the $18 subscriptions and sold a total of 33 subscriptions. If her total sales amounted to $591, how many $15 subscriptions did Mildred sell?

Question

Mildred sold magazine subscriptions with three prices: $22, $18, and $15. She sold 2 fewer of the $22 subscriptions than of the $18 subscriptions and sold a total of 33 subscriptions. If her total sales amounted to $591, how many $15 subscriptions did Mildred sell?

Answer 1

number of $18's ones --> x

number of $22's ones --> x-2
number of $15's ones --> 33 - (x + x-2) = 35 - 2x

solve ...
18x + 22(x-2) + 15(35-2x) = 591

Answer 2

To solve this problem, we can set up a system of equations. Let's define the variables:

Let x be the number of $18 subscriptions sold.
Then, the number of $22 subscriptions sold would be x - 2 (since she sold 2 fewer of the $22 subscriptions than of the $18 subscriptions).
Finally, let y be the number of $15 subscriptions sold.

We can now form the equations based on the given information:

x + (x - 2) + y = 33 (Total number of subscriptions sold is 33).
18x + 22(x - 2) + 15y = 591 (Total sales amount to $591).

Let's simplify the equations and solve the system:

x + x - 2 + y = 33 (Combining like terms).
2x - 2 + y = 33 (Simplifying).

18x + 22x - 44 + 15y = 591 (Distributing and combining like terms).
40x + 15y = 635 (Simplifying).

Now, we have a system of two equations:

2x + y = 35 (Equation 1).
40x + 15y = 635 (Equation 2).

To solve this system of equations, we can use the substitution method or elimination method. Let's use the elimination method to eliminate the variable y:

Multiply equation 1 by 15 and equation 2 by 2 to make the coefficients of y the same:

30x + 15y = 525 (Multiplying equation 1 by 15).
80x + 30y = 1270 (Multiplying equation 2 by 2).

Now, subtract equation 1 from equation 2:

(80x + 30y) - (30x + 15y) = 1270 - 525
50x + 15y = 745

Now we have a new equation:

50x + 15y = 745 (Equation 3).

Let's solve this new equation:

Subtract equation 3 from equation 2:

(40x + 15y) - (50x + 15y) = 635 - 745
40x + 15y - 50x - 15y = -110
-10x = -110
x = 11

Now that we have the value for x, we can substitute it back into equation 1 to find y:

2x + y = 35
2(11) + y = 35
22 + y = 35
y = 35 - 22
y = 13

Therefore, Mildred sold 13 subscriptions at $15.