I used the guess and check method for solving this problem but would like to know how to set up the equation. A camp counselor buys granola bars and juice drinks for the campers. She decides to buy 3 times as many drinks as granola bars. Predict how many of each she can buy on a budget of $24. Granola bars are .45 and juice drinks are .65.
My answer is 10 granola bars and 30 drinks.
agree
I did guess and check and would like to know how to set up an equation.
To set up the equation in this problem, you can use the following steps:
1. Assign variables: Let's say the number of granola bars the camp counselor buys is represented by "x" and the number of juice drinks she buys is represented by "y."
2. Write the first equation: The problem states that the counselor buys 3 times as many drinks as granola bars, so you can write the equation y = 3x.
3. Write the second equation: The total cost of the granola bars and juice drinks should not exceed the budget of $24. The cost of x granola bars is 0.45x, and the cost of y juice drinks is 0.65y. So, the equation can be written as 0.45x + 0.65y ≤ 24.
Now, to solve this system of equations, you can either use substitution or elimination method. Since you already have an answer, we can check if it satisfies the equations:
Let's substitute the values you provided: x = 10 (granola bars) and y = 30 (juice drinks) into the equations:
Equation 1: y = 3x
30 = 3(10)
30 = 30 (This equation is satisfied)
Equation 2: 0.45x + 0.65y ≤ 24
0.45(10) + 0.65(30) = 4.5 + 19.5 = 24 (This equation is satisfied)
Since both equations are satisfied, your answer of 10 granola bars and 30 drinks is indeed correct.