Algebra Story problem
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The problem is asking you to choose a Strategy, which I understood as setting up an equation?? I did miss one thing in the question, so here it is correctly.
Doreen has the same number of sisters as brothers. Her brother Oscar has twice as many sisters as brothers. How many children are in the family?
Any help would be great!!
Doreen has the same number of sisters as brothers. Her brother Oscar has twice as many sisters as brothers. How many children are in the family?
Any help would be great!!
Let g = number of girls, b = number of boys.
Dorren, then, has g-1 sisters. She supposedly has the same number of sisters as brothers, and the number of brothers is the same as the number of boys. Therefore we obtain that g-1=b.
Next, Oscar has b-1 brothers and g sisters, right? So the number of Oscar's sisters is twice that of the number of brothers he has. So, g=2(b-1).
Now we have the equations:
#1) g-1=b
#2) g=2(b-1)
1 can be solved for g: g=b+1, so we have the revised equations:
#1) g=b+1
#2) g=2(b-1)
So, g=b+1 AND g=2(b-1), so b-1=2(b-1). (This is okay to do since they are both the same as g, and we know that g=g).
Now: (I'm not sure of your level of algebra so I took it step-by-step)..
b+1 = 2(b-1)
b +1 -1 = 2(b -1) 1 1 (subtract 1 from both sides)
b = 2(b-1)-1 (simplify the -1+1)
b = 2b - 2 - 1 (using the distributive property: 2(b-1) = 2*b - 2*1 = 2b-2)
b = 2b-3 (simplifying the -2+1)
b-b = 2b-3-b (subtracting b from both sides)
0 = b-3 (simplifying the b-b on the left and 2b-b on the right)
1 = b-3+3 (adding 3 to both sides)
b=3 (simplifying the -3+3)
Now, the number of boys is 3 (b=1)! And you know that g-1=3, so put in 3 for b:
g-1=b
g-1=3 (substitute in 3 for b)
g-1+1=3+1 (add 1 to both sides)
g=4 (simplifying both sides)
Thus, the total number of children is g+b or 4+3 =7.
Hope that helps,
-daon
(edited b/c of mistake found due to Denis' counter example
)
Dorren, then, has g-1 sisters. She supposedly has the same number of sisters as brothers, and the number of brothers is the same as the number of boys. Therefore we obtain that g-1=b.
Next, Oscar has b-1 brothers and g sisters, right? So the number of Oscar's sisters is twice that of the number of brothers he has. So, g=2(b-1).
Now we have the equations:
#1) g-1=b
#2) g=2(b-1)
1 can be solved for g: g=b+1, so we have the revised equations:
#1) g=b+1
#2) g=2(b-1)
So, g=b+1 AND g=2(b-1), so b-1=2(b-1). (This is okay to do since they are both the same as g, and we know that g=g).
Now: (I'm not sure of your level of algebra so I took it step-by-step)..
b+1 = 2(b-1)
b +1 -1 = 2(b -1) 1 1 (subtract 1 from both sides)
b = 2(b-1)-1 (simplify the -1+1)
b = 2b - 2 - 1 (using the distributive property: 2(b-1) = 2*b - 2*1 = 2b-2)
b = 2b-3 (simplifying the -2+1)
b-b = 2b-3-b (subtracting b from both sides)
0 = b-3 (simplifying the b-b on the left and 2b-b on the right)
1 = b-3+3 (adding 3 to both sides)
b=3 (simplifying the -3+3)
Now, the number of boys is 3 (b=1)! And you know that g-1=3, so put in 3 for b:
g-1=b
g-1=3 (substitute in 3 for b)
g-1+1=3+1 (add 1 to both sides)
g=4 (simplifying both sides)
Thus, the total number of children is g+b or 4+3 =7.
Hope that helps,
-daon
(edited b/c of mistake found due to Denis' counter example
)