Math Problem Statement

Samuel, Jason and Sean sat for a maths test in which Samuel scored 70 marks. The ratio of the marks scored by Samuel to the marks scored by Jason was 5:2, and the ratio of the marks scored by Jason to the marks scored by Sean was 4:7. What was the total marks scored by Samuel, Jason and Sean?

Solution

The problem involves three individuals: Samuel, Jason, and Sean, and their respective marks on a math test. We're given that:

  • Samuel scored 70 marks.
  • The ratio of Samuel's marks to Jason's marks is 5:25:2.
  • The ratio of Jason's marks to Sean's marks is 4:74:7.

Let's define:

  • Samuel's marks = SS (which is 70 marks),
  • Jason's marks = JJ,
  • Sean's marks = NN.

Step 1: Relating Samuel's and Jason's marks

From the given ratio, the relation between Samuel's and Jason's marks is: SJ=52\frac{S}{J} = \frac{5}{2} Substituting S=70S = 70: 70J=52\frac{70}{J} = \frac{5}{2} Cross-multiply to solve for JJ: 70×2=5×J70 \times 2 = 5 \times J J=1405=28J = \frac{140}{5} = 28 Thus, Jason scored 28 marks.

Step 2: Relating Jason's and Sean's marks

Now, using the ratio between Jason's and Sean's marks: JN=47\frac{J}{N} = \frac{4}{7} Substituting J=28J = 28: 28N=47\frac{28}{N} = \frac{4}{7} Cross-multiply to solve for NN: 28×7=4×N28 \times 7 = 4 \times N N=1964=49N = \frac{196}{4} = 49 Thus, Sean scored 49 marks.

Step 3: Calculating the total marks

Now, we sum the marks of Samuel, Jason, and Sean: S+J+N=70+28+49=147S + J + N = 70 + 28 + 49 = 147

Final Answer:

The total marks scored by Samuel, Jason, and Sean is 147.


Would you like more details on any step, or do you have further questions? Here are some related questions you could explore:

  1. How do you simplify ratios between different numbers?
  2. Can you solve a similar problem with different ratios and totals?
  3. How do you convert a ratio into a fraction or equation?
  4. How can you check the correctness of ratio-based solutions?
  5. How do you handle more than two ratios in a similar problem?

Tip: Always ensure to cross-check ratios by simplifying and testing them with original values to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Ratios
Algebra

Formulas

Cross-multiplication in ratios

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 7-9