a pack of cardinal flower seeds costs $4, and a pack of petunia flower seeds costs $2.50. you buy the same number of packs of each type of flower and spend $39. How many pack of each do you buy? write an equation to solve.
4n + 2.5n = 39
Solve for n.
To solve this problem, we need to set up a system of equations using the given information. Let's denote the number of packs of cardinal flower seeds as 'C' and the number of packs of petunia flower seeds as 'P'.
From the problem, we know:
1. The cost of a pack of cardinal flower seeds is $4, and you buy the same number of packs of each type of flower.
2. The cost of a pack of petunia flower seeds is $2.50.
3. The total amount spent is $39.
Based on the first piece of information, we can write an equation to represent the cost of the cardinal flower seeds:
Cost of cardinal flower seeds = $4 × C = 4C
Similarly, the cost of the petunia flower seeds can be represented as:
Cost of petunia flower seeds = $2.50 × P = 2.5P
Since the total amount spent is $39, we can write the equation:
Cost of cardinal flower seeds + Cost of petunia flower seeds = $39
Substituting the equations we derived earlier into the total cost equation, we have:
4C + 2.5P = 39
This equation represents the relationship between the number of packs of cardinal and petunia flower seeds.
Now, to find the values of C and P, we can solve the equation system consisting of this equation and any other relevant equation(s). However, since we only have one equation, we cannot solve for the values of C and P individually.
In this case, we can employ a method called "guess and check" or "trial and error" to find the values of C and P. Starting with a possible value for C, we can substitute it back into the equation to see if it satisfies the condition.
Let's try some values: If we assume that C is 5, then the equation becomes:
4 × 5 + 2.5P = 39
20 + 2.5P = 39
2.5P = 39 - 20
2.5P = 19
By using trial and error, we can test different values for C until we find a value that satisfies the equation.