Question

the cost of 5 party hats and 3 balloons is 34p the cost of 3 party hats and 2 balloons is 21p what is the cost of 8 party hats and 5 balloons

Answer 1

The cost of one party hat is 5p and one balloon is 3p. Using these unit costs, the cost of 8 party hats and 5 balloons is found to be 55p.

Step-by-step explanation:

You've presented a system of linear equations where the cost of a certain number of party hats and balloons have been given. To find the individual costs, we can use simultaneous equations. Firstly, let's assume the cost of a party hat is H pence and the cost of a balloon is B pence. So, from your problem, we have:

• 
  
• 5H + 3B = 34 (equation 1)
• 
  
• 3H + 2B = 21 (equation 2)

We can solve these equations by either substitution or elimination method to find the value of H and B. Once H and B are found, we calculate the cost of 8 party hats and 5 balloons using the equation: 8H + 5B = Total Cost.

Let's use the elimination method:

1. 
   
3. Multiply equation 2 by 3 and subtract equation 1 from the result to eliminate H:
4. 
   
6. (3H + 2B) * 3 = 63 -> 9H + 6B = 63 (equation 3)
7. 
   
9. 9H + 6B - (5H + 3B) = 63 - 34
10. 
    
12. 4H + 3B = 29 (equation 4)

Now, we have the new system of equations:

• 
  
• 5H + 3B = 34 (equation 1)
• 
  
• 4H + 3B = 29 (equation 4)

Subtract equation 4 from equation 1 to eliminate B:

• 
  
• (5H + 3B) - (4H + 3B) = 34 - 29
• 
  
• H = 5

Now substituting the value of H back into equation 1 or 2, we can find the value of B:

• 
  
• 5(5) + 3B = 34
• 
  
• 25 + 3B = 34
• 
  
• 3B = 9
• 
  
• B = 3

So, one party hat costs 5p and one balloon costs 3p. The cost of 8 party hats and 5 balloons is therefore:

• 
  
• 8(5) + 5(3) = 40 + 15 = 55

The cost of 8 party hats and 5 balloons is 55p.