a. Let x be the cost of each candle, and let s be the flat rate shipping fee.
b. Allie placed two orders: one for 4 candles at a cost of $35, and one for 12 candles at a cost of $49.
c. From the first order, we know that:
4x + s = 35
From the second order, we know that:
12x + s = 49
d. To find the shipping fee, we can subtract the cost of the candles from the total cost of each order. For the first order:
s = 35 - 4x
Substituting this into the second equation, we get:
12x + (35 - 4x) = 49
Simplifying and solving for x, we get:
8x = 14
x = 1.75
Substituting this value of x into the first equation to solve for s, we get:
4(1.75) + s = 35
s = 28 - 4(1.75) = 21
Therefore, the shipping fee was $21.
e. Let n be the number of candles she can get for $60. We can set up an equation based on the cost per candle:
nx + s = 60
Substituting the values we found for x and s, we get:
n(1.75) + 21 = 60
Solving for n, we get:
n = (60 - 21) / 1.75 = 22.29
Since Allie cannot buy a fraction of a candle, she can buy a maximum of 22 candles for $60.