A farmer has 100.00 and he has to buy 100 budgies blue ones cost 10.00 green ones cost 3.00 and yellow cost .50 he has to buy at least 2 yellow and he can only spend axactly 100.00. This is a fifth grade math problem. I am a grandma trying to help my 10 year old grandson. I need help pleade.
10b + 3g + .5y = 100
b+g+y = 100
There's no unique solution, but you can see that
g = 20 - 19b/5
y = 80 + 14b/5
So, it is clear that b must be a multiple of 5. Now, if b=5,
g = 20-19b/5 = 20-19 = 1
So, 5 blue, 1 green and 94 yellows works out fine.
You can't have more than 5 blues, because then 20 - 19b/5 < 0
Of course! I'm here to help you and your grandson solve this math problem. Let's break it down step by step:
1. First, let's consider the requirement of buying at least 2 yellow budgies. This means we need to include the cost of at least 2 yellow budgies in our calculations.
2. We have three types of budgies: blue, green, and yellow. Let's assign variables to represent the number of each type of budgie.
- Let's say the number of blue budgies is represented by 'b'.
- The number of green budgies is represented by 'g'.
- And the number of yellow budgies is represented by 'y'.
3. Since we need to buy a total of 100 budgies, we have the equation:
b + g + y = 100
4. Now, let's consider the cost of each type of budgie.
- Blue budgies cost $10 each, so the total cost of blue budgies is 10b.
- Green budgies cost $3 each, so the total cost of green budgies is 3g.
- Yellow budgies cost $0.50 each, and since we need to buy at least 2 yellow budgies, the total cost of yellow budgies is 0.5y + 0.5y = y.
5. The total cost of the budgies must be exactly $100. So we have the equation:
10b + 3g + y = 100
6. As mentioned earlier, we need to buy at least 2 yellow budgies. So, y ≥ 2.
7. Now, we can start solving this problem systematically. Let's try out different values for b, g, and y until we find a combination that satisfies all the conditions.
- Let's start by setting y = 2, which is the minimum required number of yellow budgies.
8. Plugging y = 2 into the equation: 10b + 3g + 2 = 100.
9. We can simplify this equation to: 10b + 3g = 98.
10. Now, we need to find whole number solutions for b and g that satisfy this equation. One way to do this is by trial and error:
- Let's try assigning b = 2 and g = 28.
Plugging these values into the equation: 10(2) + 3(28) = 98.
This solution satisfies the equation.
11. So, if the farmer buys 2 blue budgies, 28 green budgies, and 2 yellow budgies, it would meet all the given conditions.
I hope this step-by-step explanation helps you and your grandson understand how to solve this math problem!