MATHEMATICS
In a Secondary school. 80 Students play Hockey or
Football. The number that play Football is five more
than twice the number that play Hockey. If 15 students
play both games and every student in the school plays
at least one game.
Find (i) the number of student that play football
(ii). The number of students that play Hockey

Question

UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### **Given:**
- Total number of students playing at least one game (Hockey or Football): **80**
- Number of students playing both games: **15**
- The number of students playing Football is five more than twice the number of students playing Hockey.

### **Let:**
- $$ H $$ = Number of students playing **Hockey**
- $$ F $$ = Number of students playing **Football**

### **Equations:**
1. **Total students playing at least one game:**
   $$
   H + F - \text{Both} = 80
   $$
   Substituting the number who play both:
   $$
   H + F - 15 = 80 \quad \Rightarrow \quad H + F = 95 \quad \text{(Equation 1)}
   $$

2. **Relationship between Football and Hockey players:**
   $$
   F = 2H + 5 \quad \text{(Equation 2)}
   $$

### **Solving the Equations:**

Substitute Equation 2 into Equation 1:
$$
H + (2H + 5) = 95
$$
$$
3H + 5 = 95
$$
$$
3H = 90
$$
$$
H = 30
$$

Now, substitute $$ H = 30 $$ back into Equation 2:
$$
F = 2(30) + 5 = 60 + 5 = 65
$$

### **Answers:**
1. **Number of students that play Football:** $$ \boxed{65} $$
2. **Number of students that play Hockey:** $$ \boxed{30} $$
There are 30 students who play Hockey and 65 students who play Football.

Upstudy AI Solution

Answer

Solution

Given:

Let:

Equations:

Solving the Equations:

Answers:

Beyond the Answer

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