Please help with: "James bought a packet of flour to make cakes. He used an equal amount..."

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ydubrovensky4

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James bought a packet of flour to make cakes. He used an equal amount of flour for each cake. After he had used the flour to make 3 cakes, 3/4 of the packet of flour was left. He went on to bake another 5 cakes and had 1400 g of the flour left. How much flour was used for each cake?
 
Let G = total mass of the flour packet in grams

G/4 was used for 3 cakes

G-1400 was used for 8 cakes

set up an equation and solve for G, then determine the amount of flour in 1 cake
 
ydubrovensky4 said:
James bought a packet of flour to make cakes. He used an equal amount of flour for each cake. After he had used the flour to make 3 cakes, 3/4 of the packet of flour was left. He went on to bake another 5 cakes and had 1400 g of the flour left. How much flour was used for each cake?
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ydubrovensky4 said:
James bought a packet of flour to make cakes. He used an equal amount of flour for each cake. After he had used the flour to make 3 cakes, 3/4 of the packet of flour was left. He went on to bake another 5 cakes and had 1400 g of the flour left. How much flour was used for each cake?
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Another way to start would be to define two variables:
  • C = grams of flour needed for one cake
  • P = grams of flour in the packet
Then you can write two equations, one representing "After he had used the flour to make 3 cakes, 3/4 of the packet of flour was left." and another representing "He went on to bake another 5 cakes and had 1400 g of the flour left." You can quickly eliminate the variable P, and solve for C.

But in order to help more, we need to see what you have tried, and where you are stuck.
 
skeeter said:
Let G = total mass of the flour packet in grams

G/4 was used for 3 cakes

G-1400 was used for 8 cakes

set up an equation and solve for G, then determine the amount of flour in 1 cake
Click to expand...
G/4 = 3/4(G)

G = 4(3/4G)

G = 4(2100)

G = 8400



8400/8 = 1050



1400 - 1050 = 350

is 350 the answer?
 
ydubrovensky4 said:
James bought a packet of flour to make cakes. He used an equal amount of flour for each cake. After he had used the flour to make 3 cakes, 3/4 of the packet of flour was left. He went on to bake another 5 cakes and had 1400 g of the flour left. How much flour was used for each cake?
Click to expand...
If you want to try to solve this problem in "words" rather than forming and solving equations then you could adopt this approach:-

After James had made 3 cakes there was [imath]\bf\small\frac{3}{4}[/imath] of the packet of flour left. This means that he must have used [imath]\bf\small\frac{1}{4}[/imath] of the packet to make those 3 cakes ([imath]\bf\small\frac{4}{4}[/imath] - [imath]\bf\small\frac{3}{4}[/imath] = [imath]\bf\small\frac{1}{4}[/imath]) and, therefore, he is using [imath]\bf\small\frac{1}{12}[/imath] of the packet for each cake ([imath]\bf\small\frac{1}{4}[/imath] divided by 3).

(NB: [imath]\bf\small\frac{4}{4}[/imath] and [imath]\bf\small\frac{12}{12}[/imath] are both ways to represent the whole packet flour; you do see that don't you?)

Therefore, after he has made another 5 cakes (3 + 5 = 8 cakes in total) he will have used [imath]\bf\small\frac{8}{12}[/imath] of the packet of flour (8 × [imath]\bf\small\frac{1}{12}[/imath] = [imath]\bf\small\frac{8}{12}[/imath]).

This means that he has [imath]\bf\small\frac{4}{12}[/imath] of the packet left ([imath]\bf\small\frac{12}{12}[/imath] - [imath]\bf\small\frac{8}{12}[/imath] = [imath]\bf\small\frac{4}{12}[/imath]).

So the 1,400 g of flour that remain after he has baked his 8 cakes is actually [imath]\bf\small\frac{4}{12}[/imath] (or [imath]\bf\small\frac{1}{3}[/imath]) of the whole packet.

Can you now work out how much flour James was using to make each cake?
(Hint: He now has enough left ([imath]\bf\small\frac{4}{12}[/imath]) to make another four cakes, doesn't he? ?)

Please come back and tell us your answer (and show us your working too, please).

Hope that helps. ?
 
The Highlander said:
If you want to try to solve this problem in "words" rather than forming and solving equations then you could adopt this approach:-

After James had made 3 cakes there was [imath]\bf\small\frac{3}{4}[/imath] of the packet of flour left. This means that he must have used [imath]\bf\small\frac{1}{4}[/imath] of the packet to make those 3 cakes ([imath]\bf\small\frac{4}{4}[/imath] - [imath]\bf\small\frac{3}{4}[/imath] = [imath]\bf\small\frac{1}{4}[/imath]) and, therefore, he is using [imath]\bf\small\frac{1}{12}[/imath] of the packet for each cake ([imath]\bf\small\frac{1}{4}[/imath] divided by 3).

(NB: [imath]\bf\small\frac{4}{4}[/imath] and [imath]\bf\small\frac{12}{12}[/imath] are both ways to represent the whole packet flour; you do see that don't you?)

Therefore, after he has made another 5 cakes (3 + 5 = 8 cakes in total) he will have used [imath]\bf\small\frac{8}{12}[/imath] of the packet of flour (8 × [imath]\bf\small\frac{1}{12}[/imath] = [imath]\bf\small\frac{8}{12}[/imath]).

This means that he has [imath]\bf\small\frac{4}{12}[/imath] of the packet left ([imath]\bf\small\frac{12}{12}[/imath] - [imath]\bf\small\frac{8}{12}[/imath] = [imath]\bf\small\frac{4}{12}[/imath]).

So the 1,400 g of flour that remain after he has baked his 8 cakes is actually [imath]\bf\small\frac{4}{12}[/imath] (or [imath]\bf\small\frac{1}{3}[/imath]) of the whole packet.

Can you now work out how much flour James was using to make each cake?
(Hint: He now has enough left ([imath]\bf\small\frac{4}{12}[/imath]) to make another four cakes, doesn't he? ?)

Please come back and tell us your answer (and show us your working too, please).

Hope that helps. ?
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Yes, I can work out how much flour James was using to make each cake.

If 1,400 g of flour is 4/12 (or 1/3) of the whole packet, then the whole packet must have weighed 1,400 g x 3 = 4,200 g.

This means that James was using 4,200 g / 12 cakes = 350 g of flour per cake.

Therefore, the answer is 350 g.

Your explanation in words is clear and easy to understand. I especially like how you used the example of 4/4 and 12/12 to illustrate that they both represent the whole packet of flour. This helps to make the problem more concrete and easier to visualize.
 
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