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.
R = Red
G = Green
R+G = 62
(1/2)R+2G = 88
im getting a weird answer when solving for r and g! help please!
Let R be the number of reds
Let G ....
first equation: R + G = 62
second equation: (1/2)R + 2G = 88 or
R + 4G = 176 (I multiplied each term by 2)
so
R + 4G = 176
R + G = 62
subtract
3G = 114
G = 38
subbing that into the first,
R = 24
So 24 reds and 38 greens
check is 24+ 38 = 62 Yes!
is 12 + 76 = 88 ? Yes!
thank youuu(:
Welcome!
To solve this problem, we can set up a system of equations using the given information and then solve for the number of flags of each color. Let's define two variables:
R = Number of red flags in Rosie's bag
G = Number of green flags in Rosie's bag
From the problem, we know Rosie has a total of 62 miniature flags in her bag, which means the sum of the red and green flags is 62:
R + G = 62 (Equation 1)
We are also given the information that if Rosie doubled the number of green flags and halved the number of red flags, she would have a total of 88 miniature flags. This can be expressed as:
(1/2)R + 2G = 88 (Equation 2)
Now we have a system of two equations:
R + G = 62 (Equation 1)
(1/2)R + 2G = 88 (Equation 2)
To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution in this case:
From Equation 1, we can isolate R:
R = 62 - G
Now substitute R = 62 - G into Equation 2:
(1/2)(62 - G) + 2G = 88
Multiply both sides by 2 to get rid of the fraction:
62 - G + 4G = 176
Combine like terms:
3G = 114
Divide both sides by 3:
G = 38
Now substitute G = 38 back into Equation 1:
R + 38 = 62
Subtract 38 from both sides:
R = 24
Therefore, Rosie has 24 red flags and 38 green flags in her bag.
To verify this solution, we can substitute the values of R and G into Equation 2:
(1/2)(24) + 2(38) = 12 + 76 = 88
The result is indeed 88, which confirms that our solution is correct.
So, the solution to the problem is that Rosie currently has 24 flags of red color and 38 flags of green color in her bag.