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Gcse question 6 marker

Gcse question 6 marker-example-1
User Dtortola
by
7.2k points

2 Answers

4 votes

Answer:

£107.95

Explanation:

We can use a system of equations to solve this problem, with the following variables:

  • A: The number of hours Amir worked.
  • B: The number of hours Beth worked.
  • C: The number of hours Charlie worked.

We are given the following information:

  • B = 2A
  • C = A + 5
  • A + B + C = 85

We can substitute the first two equations into the third equation to get:

A + (2A) + (A + 5) = 85

Combining like terms, we get:

4A + 5 = 85

Subtracting 5 from both sides, we get:

4A + 5 - 5 = 85 - 5

4A = 80

Dividing both sides by 4, we get:


\sf (4A )/(4)= (80)/(4)

A = 20

Now that we know A, we can find B and C using the equations B = 2A and C = A + 5:

B = 2A = 2 × 20 = 40

C = A + 5 = 20 + 5 = 25

We are also given that Amir's share of the tips was £25.40. Let T be the total amount of tips received.

The ratio of the tips received by Amir, Beth, and Charlie is:

Amir:Beth:Charlie = A:B:C = 20:40:25 also 4:8:5

We can use this ratio to set up a proportion to find T:


\sf (4)/(17) T = £ 25.40

Multiplying both sides by
\sf (17)/(4), we get


\sf T = £ 25.40 * (85 )/(20)


\sf T = £107.95

Therefore, the total amount of tips received this week was £107.95.

User Laruiss
by
8.3k points
1 vote

Answer:

£107.95

Explanation:

To calculate the total amount of tips received that week, we can first set up a system of equations based on the given information to determine how many hours Amir worked that week.

Definition of variables:

  • Let x be the number of hours Amir worked.
  • Let y be the number of hours Beth worked.
  • Let z be the number of hours Charlie worked.

Given that Beth worked twice as many hours as Amir:


y = 2x

Given that Charlie worked 5 more hours than Amir:


z = x + 5

Given that the total hours worked by Amir, Beth and Charlie was 85 hours:


x+y+z=85

Therefore, we have the following system of equations:


\begin{cases}y = 2x\\z = x + 5\\x+y+z=85\end{cases}

Substitute the first and second equations into the third equation, then solve for x:


\begin{aligned}x+2x+x+5&=85\\\\4x+5&=85\\\\4x+5-5&=85-5\\\\4x&=80\\\\(4x)/(4)&=(80)/(4)\\\\x&=20\end{aligned}

Therefore, since x = 20, the number of hours Amir worked was 20 hours.

We know that Amir's share of the tips is £25.40, so we can calculate the rate of the tips per hour by dividing £25.40 by the number of hours Amir worked:


\textsf{Tips}=(\£25.40)/(20\; \sf hours)=\£1.27\;\sf per\;hour

Given that the total hours worked by the three employees was 85 hours, to calculate the total amount of tips received, simply multiply the rate by 85 hours:


\begin{aligned}\textsf{Total tips}&=\sf \£1.27\; per\;hour * 85 \;hours\\\\&=\sf \£107.95\end{aligned}

Therefore, the total amount of tips received was £107.95.

User Ninjasense
by
8.6k points

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