Raul and Rosie are playing a guessing game. Rosie tells Raul that she has 62 miniature flags in her bag, all green or red. Rosie then tells Raul that if she doubled the green flags and halved the red flags, she would have 88 miniature flags in her bag. How many flags of each color are currently in her bag? Define two variables, write a system of equations, and solve to find the number of flags of each color. Justify your answer by showing how you solved the problem.
Im not really sure how to set this up. please help(:
R = Red
G = Green
R+G = 62
(1/2)R+2G = 88
Solve for R and G.
To solve this problem, let's define two variables:
Let's say G represents the number of green flags in Rosie's bag, and R represents the number of red flags in Rosie's bag.
We are given that Rosie has a total of 62 miniature flags in her bag:
G + R = 62 --- (Equation 1)
According to the second statement, if Rosie doubled the green flags and halved the red flags, she would have a total of 88 miniature flags:
2G + (1/2)R = 88 --- (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. In this case, let's solve it using the substitution method:
From Equation 1, we have G = 62 - R.
Substituting this into Equation 2, we get:
2(62 - R) + (1/2)R = 88
Expanding the equation:
124 - 2R + (1/2)R = 88
Multiplying every term by 2 to eliminate the fraction:
248 - 4R + R = 176
Combining like terms:
248 - 3R = 176
Subtracting 248 from both sides:
-3R = -72
Dividing both sides by -3:
R = 24
Substituting this value of R back into Equation 1:
G + 24 = 62
G = 62 - 24
G = 38
Therefore, Rosie has 38 green flags and 24 red flags in her bag.