Joyce wants to mix granola and raisins together to make a snack for her class. Granola costs $2 per pound and raisins cost $4.50 per pound. Joyce is willing to spend $37.50 and wants to make 15 pounds of trail mix.
g+_______=15
2________+4.5r=______
g+ r = 15
2g + 4.5r = 37.5
To find the number of pounds of granola needed, we can use the equation:
g + r = 15 (where g represents the weight of granola and r represents the weight of raisins)
To find the total cost, we can use the equation:
2g + 4.5r = 37.50
Let's solve these equations step-by-step.
Step 1: Solve for g in terms of r in the first equation:
g = 15 - r
Now we can substitute this value of g into the second equation:
2(15 - r) + 4.5r = 37.50
Step 2: Simplify and solve for r:
30 - 2r + 4.5r = 37.50
2.5r = 7.50
r = 7.50 / 2.5
r = 3
Step 3: Substitute the value of r into the first equation to find the value of g:
g + 3 = 15
g = 12
So, Joyce needs 12 pounds of granola and 3 pounds of raisins to make 15 pounds of trail mix.
The missing values in the equations are:
g + 3 = 15
2(15 - 3) + 4.5(3) = 37.50
Thus, the missing values are 3 for the first equation and 33 for the second equation.
To find the weight of the granola and raisins that Joyce needs, we'll set up two equations. Let's represent the weight of the granola as 'g' and the weight of the raisins as 'r'.
1) The weight of the granola and raisins combined is 15 pounds:
g + r = 15
2) The total cost of the granola and raisins is $37.50:
2g + 4.5r = 37.50
Now, let's solve for the variables.
To solve the first equation for 'g', we can isolate the variable:
g = 15 - r
Now, substitute the value of 'g' in the second equation:
2(15 - r) + 4.5r = 37.50
Simplify the equation:
30 - 2r + 4.5r = 37.50
2.5r = 7.50
Divide both sides of the equation by 2.5:
r = 3
Now, substitute the value of 'r' back into the first equation to find the weight of the granola:
g + 3 = 15
g = 12
Therefore, Joyce needs 12 pounds of granola and 3 pounds of raisins to make 15 pounds of trail mix.