Farah, Kate and Jane have managed their savings well. The sum of Farah and Kate's savings is $1548. Farah and Jane's savings sum up to $1842. The ratio of Kate to Jane's savings is 4 : 7. How much has Farah saved?

Question

Illustrate an abstract image demonstrating a mathematical calculation between three people, represented by distinct shapes. Let's use a circle, a triangle, and a square. The circle (representing Farah's savings) intersects with both the triangle (representing Kate's savings) and the square (representing Jane's savings). The intersection with the triangle represents a sum of $1548 and the intersection with the square represents a sum of $1842. In addition, there's a scale symbol with the triangle on one side and the square on the other, indicating a ratio of 4 to 7.

Farah, Kate and Jane have managed their savings well. The sum of Farah and Kate's savings is $1548. Farah and Jane's savings sum up to $1842. The ratio of Kate to Jane's savings is 4 : 7. How much has Farah saved?

Answer 1

= 1548

f+j = 1842
subtract those two equations:
j-k = 294
j = 294 + k

k/j = 4/7
4j = 7k
j = 7k/4

sub into j = 294+k
7k/4 = 294 + k
times 4
7k = 1176 + 4k
3k=1176
k = 392

then j = (7/4)(392) = 686
f+j = 1842
f = 1156

Answer 2

Delvin, Eric and Felicia have 478 stickers.

Delvin has 4 times as many stickers as Eric.
Felicia has 397 stickers more than Delvin.
How many stickers does Delvin have?

Answer 3

Let's assign variables for the amount saved by each person:

Let F be the amount Farah has saved.
Let K be the amount Kate has saved.
Let J be the amount Jane has saved.

From the given information, we can write the following equations:

Equation 1: F + K = 1548
Equation 2: F + J = 1842
Equation 3: K/J = 4/7

To solve this system of equations, we will use the elimination method.

From Equation 3, we can rewrite it as K = (4/7)J.

Substituting this expression for K into Equation 1, we get:

F + (4/7)J = 1548 ........(Equation 4)

Substituting the expression for F from Equation 2 into Equation 4, we get:

(1842 - J) + (4/7)J = 1548

Multiplying both sides by 7 to eliminate the fraction, we have:

7(1842 - J) + 4J = 7(1548)
12894 - 7J + 4J = 10836
3J = 10836 - 12894
3J = -2058
J = -2058/3
J = -686

Since we cannot have negative savings, it means there's an error in the problem or the given information. Please check the values again to ensure they are correct.

If you have any further questions, feel free to ask!

Answer 4

To find out how much Farah has saved, let's break down the information provided and solve step by step.

Let's assign variables:
Let F be the amount Farah has saved.
Let K be the amount Kate has saved.
Let J be the amount Jane has saved.

From the information given, we can create the following equations:

1. Farah + Kate = $1548
F + K = 1548

2. Farah + Jane = $1842
F + J = 1842

3. The ratio of Kate to Jane's savings is 4 : 7.
K/J = 4/7

To solve the system of equations, we can use substitution or elimination method. Let's use substitution:

From equation 3, we have K/J = 4/7, which can be rearranged as K = (4/7)J.

Substituting this into equation 1, we get:
F + (4/7)J = 1548 -----> Eq. 4

Substituting this into equation 2, we get:
F + J = 1842 -----> Eq. 5

Now, we can solve equations 4 and 5 simultaneously to find the values of F and J.

Subtracting equation 5 from equation 4, we get:
(4/7)J - J = 1548 - 1842
(4/7 - 1)J = -294
(-3/7)J = -294

Multiplying both sides by -7/3, we get:
J = (-294) * (-7/3)
J = 686

Now that we have found the value of J (Jane's savings), we can substitute it back into equation 5 to find the value of F (Farah's savings).

F + 686 = 1842
F = 1842 - 686
F = 1156

Therefore, Farah has saved $1156.