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Ahmed worked all summer for a bee farmer. Ahmed was paid $400.00 the first week. The farmer paid a $50.00 raise per week for each additional week of employment. Ahmed worked on the bee farm for 8 weeks before his first year of university began.

The money Ahmed earned over the summer was used for miscellaneous expenses at university. At the start of the ninth week of school he had $3 000.00 in his bank account. How much money did Ahmed spend each week?

The school year is approximately 32 weeks long. Will Ahmed have enough money if he continues to spend his savings at the same rate?

4 years ago

## Answered By Anna S

1. We have to calculate how much Ahmed earned on the bee farm. Since the farmer paid raise $50.00 per week, we know that it is and arithmetic progression with first term a

_{1}= 400 , difference d = 50 and number of terms n = 8Since we have to calculate the total amount earned we will use the formula for the sum of 8-terms S

_{8}= n/2 * (a_{1}+ a_{n}) where a_{n}= a_{1}+ (n - 1)*dTherefore S

_{8}= 8/2 * {a_{1 }+ [a_{1}+ (n-1) *d]}S

_{8}= 8/2 * { 400 + [400 + (8 - 1)*50]}S

_{8}= 4 * { 400 + [ 400 + 350]}S

_{8}= 4 * 1,150 = $4,600.00Ahmed totally earned $4,600 on bee farm.

2. We will calculate if Ahmed will have enough money for the school year if he will spent them at the same rate as the first 8 weeks of the school (" the start of the ninth week").

Ahmed earned in total............$4,600.00

At the start of 9th wee left......( 3,000.00)

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Ahmed spending for 8 weeks $1,600.00 Therefore $1,600.00 / 8 = $200 per week

School year ..................32 weeks long

already passed............ 8 weeks

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still left 24 week @ $200 per week = 24* 200 = $4,800

Ahmed has left $3,000 at the beginning of the ninth week, therefore he will not have enough money at the current rate of spending.