Colin paid �$4 for 4 buns and 4 cakes. 3 buns cost as many as 2 cakes.What was the total cost of 5 buns and 5 cakes? (My teacher gave this to my class as a brainteaser. I'm Australian and I'm nowhere near the smartest in my class. My homework is due in 6 hours. I've been taking tutoring classes for atleast 6 years now, I'm in grade 5.)
4b+4c=4
3b = 2c, so substitute that into the first equation
4b+6b=4
10b=4
b=$0.40
3b= $1.20, so 2c=$1.20, and c=$0.60
If 4 buns and 4 cakes cost $4 ,then
1 buns and 1 cake costs $1
--> 4b + 4c = 4
b + c = 1
you want 5 buns + 5 cakes
= 5b + 5c
= 5(b+c)
= 5(1) = $5
The fact that 3 buns cost as much as 2 cakes is not needed and is simply a distraction.
It would matter only if you needed the actual cost of a bun and a cake, but that was not asked for.
Nice little question.
Olivia, most of the math tutors on here live in the US and Canada, so you posted at 1:47 am our time, which means most of them were probably asleep.
So you missed your 6 hour deadline. Keep the time difference in mind for next time
Let's break down the information given step-by-step to find the solution:
1. Colin paid $4 for 4 buns and 4 cakes. This means that the cost of each bun or each cake is $4/4 = $1.
2. It is stated that 3 buns cost as many as 2 cakes. So, the cost of 3 buns is equal to the cost of 2 cakes.
3. Since the cost of each bun is $1, the cost of 3 buns is 3 * $1 = $3.
4. Therefore, the cost of 2 cakes is also $3.
5. To find the cost of 1 cake, we can divide the cost of 2 cakes ($3) by 2. The cost of 1 cake is $3/2 = $1.50.
6. Now that we know the cost of 1 bun is $1 and the cost of 1 cake is $1.50, we can determine the total cost of 5 buns and 5 cakes.
7. The cost of 5 buns is 5 * $1 = $5.
8. The cost of 5 cakes is 5 * $1.50 = $7.50.
9. To find the total cost of 5 buns and 5 cakes, we add the individual costs together: $5 + $7.50 = $12.50.
Therefore, the total cost of 5 buns and 5 cakes is $12.50.
To solve this problem, let's break it down step by step:
1. We know that Colin paid $4 for 4 buns and 4 cakes. Let's assume the cost of each bun is x dollars and the cost of each cake is y dollars.
2. From the information given, we can set up two equations. The first equation represents the total cost of 4 buns and 4 cakes, which is $4:
4x + 4y = 4
3. We also know that 3 buns cost as many as 2 cakes. This can be represented by the second equation:
3x = 2y
Now, we need to find the values of x and y that satisfy both equations.
To solve this system of equations, we'll use the substitution method:
Step 1: Solve the second equation for x in terms of y:
x = (2y) / 3
Step 2: Substitute this value of x in the first equation:
4((2y) / 3) + 4y = 4
Simplifying this equation gives you:
(8y / 3) + 4y = 4
(8y + 12y) / 3 = 4
20y / 3 = 4
Multiplying both sides by 3 gives you:
20y = 12
Dividing both sides by 20 gives you:
y = 0.6
Step 3: Substitute the value of y back into the second equation to find x:
3x = 2(0.6)
3x = 1.2
Dividing both sides by 3 gives you:
x = 0.4
So, the cost of each bun (x) is $0.4 and the cost of each cake (y) is $0.6.
Now, let's calculate the total cost of 5 buns and 5 cakes:
Total cost of 5 buns = 5 * $0.4 = $2
Total cost of 5 cakes = 5 * $0.6 = $3
Therefore, the total cost of 5 buns and 5 cakes is $2 + $3 = $5.
In conclusion, the total cost of buying 5 buns and 5 cakes would be $5.