Victoria spends 5/9 of her money of a flan and two chicken pies. Each chicken pie cost 1/6 as much as the flan. Victoria has $24 left.
a. How much money does Victoria spend?
b. How much does the flan cost?
M = Her money
If she spends 5 / 9 of her money the rest is 4 / 9 of her money.
Victoria has $24 left means:
4 M / 9 = $24
Multiply both sides by 9
4 M = $216
Divide both sides by 4
M = $54
Victoria spend 5 * $54 / 9 = $30
F = Price of flan
C = Price of chicken pie
Each chicken pie cost 1 / 6 as much as the flan means:
C = F / 6
Victoria spends 5 / 9 of her money of a flan and two chicken pies means:
5 M / 9 = F + 2 C
Replace C = F / 6 in this equation
5 M / 9 = F + 2 * F / 6
5 M / 9 = F + 2 * F / 2 * 3
5 M / 9 = F + F / 3
5 M / 9 = 3 F / 3 + F / 3
5 * 54 / 9 = 4 F / 3
$ 270 / 9 = 4 F / 3
$ 30 = 4 F / 3
Multiply both sides by 3
$ 90 = 4 F
Divide both sides by 4
$22.5 = F
F = $22.5
a.
Victoria spend $30
b.
The flan cost $22.5
a. Well, if Victoria has $24 left, then we can assume she spent some money before that. Let's call the amount she spent X. Now, we know that 5/9 of X went towards a flan and two chicken pies.
So, the amount spent on the flan and two chicken pies would be 5/9 times X.
The remaining amount, which is $24, would be 4/9 times X (since 9/9 - 5/9 = 4/9).
Therefore, we can set up the equation:
4/9 * X = $24
Now, we can solve for X, which is the total amount spent by Victoria.
b. Since we know the total amount spent by Victoria is X, and the amount spent on the flan and two chicken pies is 5/9 times X, we can find the cost of the flan by multiplying that amount by its ratio to the chicken pies.
Given that each chicken pie costs 1/6 as much as the flan, we can set up the equation:
(5/9 * X) = flan cost
(1/6) * (5/9 * X) = flan cost
Solving this equation will give us the cost of the flan.
To find out how much money Victoria spends, we need to first determine the cost of the flan and the chicken pies.
Let's assume that Victoria's total money is represented by variable 'x'. Therefore, she spends 5/9 of x on the flan and two chicken pies.
Since each chicken pie costs 1/6 as much as the flan, the total cost of the chicken pies would be (1/6) * (5/9) * x.
Now, let's calculate the total money spent by Victoria:
Money spent = Cost of flan + Cost of chicken pies
Money spent = (5/9) * x + (1/6) * (5/9) * x
We know that Victoria has $24 left, so we can equate the money spent to her remaining money:
Money spent + $24 = x
Now, let's solve these equations to answer the given questions.
a. How much money does Victoria spend?
Substitute the expression for money spent into the equation for remaining money:
(5/9) * x + (1/6) * (5/9) * x + $24 = x
Multiply through by the common denominator of 9 to eliminate the fractions:
(5/9) * 9 * x + (1/6) * (5/9) * 9 * x + $24 * 9 = 9 * x
5 * x + (5/6) * 5 * x + $216 = 9 * x
5x + (25/6) * x + $216 = 9x
Combining like terms:
5x + (25/6) * x - 9x = -$216
(30x + 25x - 54x)/6 = -$216
(55x - 54x)/6 = -$216
x/6 = -$216
Multiply through by 6 to solve for x:
x = -$216 * 6
x = -$1296
Since x represents Victoria's total money, we cannot have negative money. Therefore, the given information may not be feasible.
b. How much does the flan cost?
If the given information is not feasible, then we cannot determine the cost of the flan.
To find the answers to these questions, we can break it down step by step.
Let's start with part a), "How much money does Victoria spend?"
Let's assume Victoria's total amount of money is M dollars.
From the given information, we know that Victoria spends 5/9 of her money on a flan and two chicken pies. This means that 5/9 of her money is equal to the cost of the flan and two chicken pies combined.
Now we also know that each chicken pie costs 1/6 as much as the flan. Let's say the cost of the flan is F dollars. Therefore, the cost of each chicken pie is 1/6 * F dollars.
So, the total amount of money spent on the flan and two chicken pies is F + 2 * (1/6 * F).
Since this total amount spent is 5/9 of Victoria's money, we can write the following equation:
5/9 * M = F + 2 * (1/6 * F)
Now we can solve this equation to find the value of M, which represents the total amount of money Victoria had in the beginning.
To do that, let's simplify the equation:
5/9 * M = F + 1/3 * F
We can combine the terms on the right side:
5/9 * M = 4/3 * F
Now, let's isolate M:
M = (4/3 * F) / (5/9)
We can simplify this expression by multiplying the numerator and denominator by 9/5:
M = 4/3 * F * 9/5
M = (36/15) * F
M = 12/5 * F
Therefore, we can say that the total amount of money Victoria had in the beginning is 12/5 times the cost of the flan.
Now, let's move on to part b), "How much does the flan cost?"
From the equation above, we found that M = 12/5 * F.
We also know that Victoria has $24 left. So, the remaining amount of money she has is $24.
Therefore, we can set up another equation:
M - (F + 2 * (1/6 * F)) = $24
Substituting the value of M from the previous equation:
(12/5 * F) - (F + 2 * (1/6 * F)) = $24
We can simplify this equation:
12/5 * F - F - (1/3 * F) = $24
Multiplying all terms by 15 to get rid of fractions:
36F - 15F - 5F = $360
16F = $360
Dividing both sides by 16:
F = $360 / 16
F = $22.5
Therefore, the cost of the flan is $22.5.
To summarize:
a) Victoria spends 5/9 * M dollars, which is 12/5 times the cost of the flan.
b) The cost of the flan is $22.5.