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| Math Central | Quandaries & Queries |
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Question from Varsha, a student: A province's Ministry of Social services has found that both the number of people needing social assistance and the province's total expenditures on social assistance are proportional to the rate of unemployment. Last August when the provincial unemployment rate was 8.4 %, the province provided assistance to 89,300 individuals at a total cost of 4107.4 million. The forecast unemployment rate for next August is 7.9%. How many people can the province expect to need social assistance next August? What amount should the province budget for social assistance in August? |
Varsha,
Since the number of people needing social assistance is proportional to the rate of unemployment there is a number $k$ so that
\[\mbox{(the number of people needing social assistance) } = k \times \mbox{( the rate of unemployment)} \]
Substitute the values from last August into this expression and solve for $k.$
Now that you know the value of $k$ substitute it and the forecast unemployment rate for next August into the expression and solve for the number of people expected to be on social assistance next August.
Perform similar calculations for the total cost of the social assistance program.
Penny
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