g+ r = 15
2g + 4.5r = 37.5
g+_______=15
2________+4.5r=______
2g + 4.5r = 37.5
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.
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.