A bakery collected $1848 from selling some pies and cakes. The ratio of money collected from selling the pies to cakes was 15 :7. The ratio of the number of pies to cakes sold was 4:1. A cake cost $13 more than a pie. How many cakes were sold?
Let's assume the number of pies sold as 4x and the number of cakes sold as x.
The ratio of money collected from selling the pies to cakes is 15:7, so we can set up the equation:
15/7 = (4x * p) / (1x * (p+13))
Cross-multiplying will give us:
15 * x * (p+13) = 7 * 4x * p
Expanding the equation:
15xp + 15 * 13x = 28xp
15xp - 28xp = -15 * 13x
-13xp = -15 * 13x
-xp = -15
Dividing both sides by -x, we get the value of p:
p = -15 / -x
p = 15
Since we assumed the number of cakes sold as x, we get:
x = 15
Therefore, the number of cakes sold is 15.
To solve this problem, we need to break it down into smaller steps.
Step 1: Find the ratio of the money collected from selling pies to cakes.
The ratio of money collected from selling pies to cakes is given as 15:7.
Step 2: Find the ratio of the number of pies to cakes sold.
The ratio of the number of pies to cakes sold is given as 4:1.
Step 3: Determine the cost difference between a pie and a cake.
It is given that a cake costs $13 more than a pie.
Step 4: Assign variables to the quantities we need to find.
Let's assume the cost of a pie is "x" dollars, and the cost of a cake is "x + 13" dollars.
Step 5: Set up an equation for the total amount collected from selling pies and cakes.
We can now set up an equation based on the information given. Since the money collected from selling pies and cakes is $1848, we can write:
15x + 7(x + 13) = 1848
Step 6: Solve the equation to find the value of x.
Simplifying the equation:
15x + 7x + 91 = 1848
22x + 91 = 1848
22x = 1757
x = 79.86 (rounded to 2 decimal places)
Step 7: Calculate the number of cakes sold.
Since the ratio of pies to cakes sold is 4:1, we can determine the number of cakes sold by multiplying the number of pies (4) by the ratio of cakes to pies (1/4). This gives us:
4 * (1/4) = 1
Therefore, 1 cake was sold.
Total income = 1848
income from pies : income from cakes = 15:7
income from pies = 1848/22*15 = 1260
income from cakes = 1848/22*7 = 588
price:
price of pie ---- y
price of cake ---- y + 13
number:
pies --- 4x
cakes --- x
4xy = 1260 , #1 ----> xy = 315
and
x(y+13) = 588
xy + 13x = 588 , #2
but xy = 315
into #2, 315 + 13x = 588
13x = 273
x = 21
and that makes y = 15 , from #1
Now look at my definitions and state your conclusion
Nice ratio question!