Jacob baked some cupcakes. He gave 1/7 to his neighbour and 27 to his aunt.
He had 15 cupcakes left.
(a) What fraction of the cupcakes did Jacob have remaining after giving to his neighbour?
(b) How many cupcakes did Jacob give to his neighbour?
(a) To find the fraction of cupcakes Jacob had remaining after giving to his neighbor, we need to subtract the number of cupcakes he gave away from the total number of cupcakes he started with.
Let's denote the total number of cupcakes Jacob had as T. We know that T - 1/7 T - 27 = 15.
Simplifying this equation, we have 6/7 T - 27 = 15.
Adding 27 to both sides, we get 6/7 T = 42.
Finally, dividing both sides by 6/7, we find T = 49.
So, Jacob had 15/49 of the cupcakes remaining after giving to his neighbor.
(b) Jacob gave 1/7 of his cupcakes to his neighbor. From the previous calculation, we know that Jacob had a total of 49 cupcakes. To find the number of cupcakes he gave to his neighbor, we can simply calculate 1/7 of 49.
1/7 * 49 = 7 cupcakes.
Therefore, Jacob gave 7 cupcakes to his neighbor.
(a) To find the fraction of cupcakes Jacob had remaining after giving some to his neighbor, we need to subtract the fraction he gave away from 1.
Jacob gave away 1/7 of the cupcakes, so the fraction he has left is 1 - 1/7.
To subtract fractions, we need a common denominator. In this case, the common denominator is 7.
So, we have (7/7) - (1/7) = 6/7.
Therefore, Jacob had 6/7 of the cupcakes remaining after giving some to his neighbor.
(b) To determine how many cupcakes Jacob gave to his neighbor, we can start by subtracting the number of cupcakes he gave to his aunt and the number of cupcakes he had left from the total number of cupcakes he baked.
Jacob baked a certain number of cupcakes, but the exact quantity is not mentioned in the question. Let's represent this unknown quantity as "x."
According to the information provided, Jacob gave 1/7 of the cupcakes to his neighbor. This can be expressed as (1/7)x. Additionally, he gave 27 cupcakes to his aunt. Therefore, the total number of cupcakes given away is (1/7)x + 27.
The remaining cupcakes that Jacob had can be represented as 15.
So, we can set up an equation to solve for x:
x - [(1/7)x + 27] = 15
To simplify the equation, we can distribute the negative sign:
x - (1/7)x - 27 = 15
Next, we combine like terms:
(6/7)x - 27 = 15
To isolate x, we add 27 to both sides of the equation:
(6/7)x = 42
Finally, we multiply both sides by the reciprocal of (6/7), which is (7/6):
x = (42)(7/6) = 49
Therefore, Jacob baked a total of 49 cupcakes.
To find out how many cupcakes he gave to his neighbor, we substitute this value into the expression (1/7)x:
(1/7)(49) = 7
Thus, Jacob gave 7 cupcakes to his neighbor.
Apologies for the mistake in my previous response. Your explanation is correct.
Jacob gave 1/7 of the cupcakes to his neighbor, so the fraction he has left is 1 - 1/7 = 6/7.
Therefore, Jacob had 6/7 of the cupcakes remaining after giving some to his neighbor.
To determine how many cupcakes Jacob gave to his neighbor, we can subtract the number of cupcakes he had left (15) from the total number of cupcakes he baked.
Jacob baked a total of: 15 cupcakes (left) + 27 cupcakes (given to his aunt) = 42 cupcakes.
Hence, Jacob gave 42 cupcakes - 15 cupcakes = 27 cupcakes to his neighbor.
You are correct on (b). It was 7 cupcakes
I apologize for the confusion caused. Thank you for pointing out the error. Yes, Jacob gave 7 cupcakes to his neighbor. Thank you for your understanding.
(a) To find the fraction of cupcakes Jacob had remaining after giving to his neighbor, we need to subtract the amount he gave (1/7) from the total amount he had initially.
Total cupcakes = 27 + 15 = 42
Cupcakes remaining = 42 - 1/7 * 42 = 42 - 6 = 36
So, Jacob had 36/42 cupcakes remaining.
(b) Jacob gave 1/7 of his cupcakes to his neighbor. To find the number of cupcakes, we multiply the fraction (1/7) by the total number of cupcakes he had initially.
Cupcakes given to neighbor = 1/7 * 42 = 6
Jacob gave 6 cupcakes to his neighbor.
To find the answer to part (a), we need to determine the fraction of cupcakes that Jacob had remaining after giving some to his neighbor. We can do this by subtracting the fraction he gave away from 1 (since 1 represents the entire initial amount of cupcakes).
(a) Fraction remaining after giving to neighbor = 1 - (Fraction given to neighbor)
Jacob gave 1/7 of the cupcakes to his neighbor, so we subtract 1/7 from 1:
Fraction remaining after giving to neighbor = 1 - 1/7
To subtract fractions, we need the same denominator. We can convert 1 to a fraction with a denominator of 7:
1 = 7/7
Now we can subtract the fractions:
Fraction remaining after giving to neighbor = 7/7 - 1/7 = 6/7
Therefore, Jacob had 6/7 of the cupcakes remaining after giving 1/7 to his neighbor.
To answer part (b), we already know that Jacob had 15 cupcakes left after giving some to his neighbor and his aunt. So, to find out how many cupcakes he gave to his neighbor, we subtract the number of cupcakes left from the total number he initially had:
(b) Cupcakes given to neighbor = Total cupcakes - Cupcakes remaining
= 27 - 15
= 12
Therefore, Jacob gave 12 cupcakes to his neighbor.