Question 423217: twenty-six students entered their projects in the science fair. the number of girls was 4 fewer than twice the number of boys. how many boysand how manygirls entered their projects in the fair?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Always start by turning the words into sentences that are easier to understand.
g = number of girls
b = number of boys
.
The number of girls is 4 fewer than 2 times the number of boys.
In other words, the number of girls equals 2 times the number of boys minus 4.
g = 2b - 4
.
The total number of entrants equals 26.
Of course, the total number of entrants equals the number of girls plus the number of boys.
26 = g + b
Alternately, we can say:
g = 26 - b
or
b = 26 - g
.
Looking back, we know...
g = 2b - 4
and
g = 26 - b
so, we can substitute...
g = g
which means
2b -4 = 26 - b
adding b to both sides
3b -4 = 26
adding 4 to both sides
3b = 30
dividing both sides by 3
b = 10
.
From above we know:
g = 26 - b
g = 26 - 10
g = 16
.
Always check your work!
.
Does the number of girls equal two times the number of boys minus 4?
g = 2*10 -4
g = 20 - 4
g = 16
That checks.
.
Remember to state your answer clearly.
The number of boys equals 10. The number of girls euqals 16.
.
Done.
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