Answer :
Let's solve the problem step-by-step.
We have three people: A, B, and C. The amounts of money they receive are in the ratio 4:7. Additionally, it's given that A receives R 500 less than C.
1. Express in terms of variables:
- Let the amount A receives be [tex]\(4x\)[/tex].
- Since the ratio for B hasn't been fully specified, let's consider B initially also as a multiple of [tex]\(x\)[/tex], but focus on solving for A and C first.
- A receives R 500 less than C. Therefore, we can express the amount C receives as [tex]\(4x + 500\)[/tex].
2. Set up the relationship for C:
- We know that C initially should be related to the ratio. Given the problem aligns the ratio as 4:7 for A and indirectly describes the relationship between A and C, we evaluate using C's relationship to [tex]\(7x\)[/tex], from the undeclared action in the ratio.
- Therefore, C's share should equate to the expression of their combined conceptual meaning in the ratio form.
3. Equate the expressions for C and solve for [tex]\(x\)[/tex]:
- C's amount can also be defined as the second part of the ratio, being [tex]\(7x\)[/tex].
- Hence, [tex]\(7x = 4x + 500\)[/tex].
4. Solve for [tex]\(x\)[/tex]:
- Subtract [tex]\(4x\)[/tex] from both sides: [tex]\(7x - 4x = 500\)[/tex].
- This simplifies to: [tex]\(3x = 500\)[/tex].
- Dividing both sides by 3 gives: [tex]\(x = \frac{500}{3}\)[/tex] or approximately [tex]\(166.67\)[/tex].
5. Calculate the individual amounts:
- A's share is [tex]\(4x = 4 \times 166.67 = R 666.67\)[/tex].
- C's share is [tex]\(7x = 7 \times 166.67 = R 1166.67\)[/tex].
6. Find the total amount:
- The sum of the money A and C receive would be [tex]\(A + 500 + C\)[/tex], plugging in the values:
- This results in approximately [tex]\(666.67 + 166.67 + 1166.67 = R 2333.33\)[/tex].
Therefore, the total amount divided amongst A, B, and C is approximately R 2333.33.
We have three people: A, B, and C. The amounts of money they receive are in the ratio 4:7. Additionally, it's given that A receives R 500 less than C.
1. Express in terms of variables:
- Let the amount A receives be [tex]\(4x\)[/tex].
- Since the ratio for B hasn't been fully specified, let's consider B initially also as a multiple of [tex]\(x\)[/tex], but focus on solving for A and C first.
- A receives R 500 less than C. Therefore, we can express the amount C receives as [tex]\(4x + 500\)[/tex].
2. Set up the relationship for C:
- We know that C initially should be related to the ratio. Given the problem aligns the ratio as 4:7 for A and indirectly describes the relationship between A and C, we evaluate using C's relationship to [tex]\(7x\)[/tex], from the undeclared action in the ratio.
- Therefore, C's share should equate to the expression of their combined conceptual meaning in the ratio form.
3. Equate the expressions for C and solve for [tex]\(x\)[/tex]:
- C's amount can also be defined as the second part of the ratio, being [tex]\(7x\)[/tex].
- Hence, [tex]\(7x = 4x + 500\)[/tex].
4. Solve for [tex]\(x\)[/tex]:
- Subtract [tex]\(4x\)[/tex] from both sides: [tex]\(7x - 4x = 500\)[/tex].
- This simplifies to: [tex]\(3x = 500\)[/tex].
- Dividing both sides by 3 gives: [tex]\(x = \frac{500}{3}\)[/tex] or approximately [tex]\(166.67\)[/tex].
5. Calculate the individual amounts:
- A's share is [tex]\(4x = 4 \times 166.67 = R 666.67\)[/tex].
- C's share is [tex]\(7x = 7 \times 166.67 = R 1166.67\)[/tex].
6. Find the total amount:
- The sum of the money A and C receive would be [tex]\(A + 500 + C\)[/tex], plugging in the values:
- This results in approximately [tex]\(666.67 + 166.67 + 1166.67 = R 2333.33\)[/tex].
Therefore, the total amount divided amongst A, B, and C is approximately R 2333.33.
