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The number of boys plus the number of girls equals 350.
20
There are 350 students taking algebra and the ratio of boys to girls is 33:37. We need to find how many more girls than boys are taking the course. To do so we will write and solve a system of equations.
The ratio of boys to girlscan be written as bg. This fraction we have been told is equal to 33:37= 3337.
b/g=33/37 By combining these we find our system of equations. b+ g=350 & (I) b g= 3337 & (II)
(II): LHS * g=RHS* g
(II): a/c* b = a* b/c
(I): b= 33g/37
(I): a = 37* a/37
(I): Add fractions
(I): LHS * 37=RHS* 37
(I): .LHS /70.=.RHS /70.
(I): g= 185
(I): Calculate quotient and product
We can interpret this solution, b= 165 and g= 185, as follows. The number of $ boys$ taking algebra is $ 165.$ The number of $ girls$ taking algebra is $ 185.$ The question asks how many more girls than boys are taking the course, so our answer will be 185- 165=20.