Quiz 1
Word problems fundamentals practice
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The original price of a laptop was increased by $$25\%$$. In March, the new price was reduced by $$20\%$$. In April, a coupon of $$\$40$$ was applied. The final price paid was $$140$$ dollars. What was the original price of the laptop?⌄
Let the original price be $$x$$.After a $$25\%$$ increase: $$1.25x$$After a $$20\%$$ reduction:$$0.8(1.25x)=x$$So, the price returns to the original price.Then a coupon of $$\$40$$ is applied.$$x-40=140$$$$x=180$$Final answer: $$180$$
In a company, each employee receives a performance score from $$0$$ to $$100$$. The average score of male employees is $$70$$. The average score of all employees is $$76$$. There are $$30$$ male employees and $$20$$ female employees. What is the average score of the female employees?⌄
Total employees:$$30+20=50$$Total score of all employees:$$50\cdot76=3800$$Total score of male employees:$$30\cdot70=2100$$Total score of female employees:$$3800-2100=1700$$Average score of female employees:$$\frac{1700}{20}=85$$Final answer: $$85$$
In a firm: $$60\%$$ of employees are in sales. $$25\%$$ are in engineering. $$15\%$$ are in management. Sales average salary is $$50{,}000$$ dollars. Engineering average salary is $$90{,}000$$ dollars. Overall average salary is $$80{,}000$$ dollars. What is the average salary of management?⌄
Use a weighted average.$$0.60(50000)+0.25(90000)+0.15(m)=80000$$$$30000+22500+0.15m=80000$$$$52500+0.15m=80000$$$$0.15m=27500$$$$m=\frac{27500}{0.15}$$$$m=183333.33\ldots$$Final answer: $$183333$$
A car travels the first $$240$$ miles of a trip at $$60$$ miles per hour. How fast must the car travel the remaining $$120$$ miles so that the total trip time is $$5$$ hours?⌄
Time for first part:$$\frac{240}{60}=4$$Remaining time:$$5-4=1$$Required speed for remaining $$120$$ miles:$$\frac{120}{1}=120$$Final answer: $$120$$
If one worker can complete a job in $$10$$ minutes and another worker can complete the same job in $$15$$ minutes, how many minutes will it take them working together to complete the job?⌄
Work rate of first worker:$$\frac{1}{10}$$Work rate of second worker:$$\frac{1}{15}$$Combined rate:$$\frac{1}{10}+\frac{1}{15}=\frac{3}{30}+\frac{2}{30}=\frac{5}{30}=\frac{1}{6}$$Time for one job: $$6$$Final answer: $$6$$
A farmer planted $$3$$ times as many corn seeds as wheat seeds. $$20\%$$ of the corn seeds grew into plants, and $$25\%$$ of the wheat seeds grew into plants. If a total of $$350$$ plants grew, how many wheat seeds were planted?⌄
Let the number of wheat seeds be $$w$$.Then the number of corn seeds is $$3w$$Plants from corn:$$0.20(3w)=0.6w$$Plants from wheat:$$0.25w$$Total plants:$$0.6w+0.25w=350$$$$0.85w=350$$$$w=\frac{350}{0.85}=\frac{7000}{17}\approx411.76$$Final answer: $$412$$
A container holds $$6$$ quarts of alcohol and $$3$$ quarts of water. How many quarts of water must be added to create a mixture that is $$2$$ parts alcohol to $$3$$ parts water by volume?⌄
Let the number of quarts of water added be $$x$$.Alcohol stays $$6$$Water becomes $$3+x$$Set the ratio.$$\frac{6}{3+x}=\frac{2}{3}$$Cross-multiply.$$18=2(3+x)$$$$18=6+2x$$$$12=2x$$$$x=6$$Final answer: $$6$$
The sum of the pre-tax costs of Item A and Item B is $$400$$ dollars. In one city, each item is taxed at a flat $$5\%$$. In another city, Item A is taxed at $$8\%$$ and Item B is taxed at $$12\%$$. If the total tax in the second city is $$8$$ dollars more than in the first city, what is the pre-tax price of Item A?⌄
Let the pre-tax price of Item A be $$A$$.Then the pre-tax price of Item B is $$400-A$$Tax in the first city:$$0.05(400)=20$$Tax in the second city:$$0.08A+0.12(400-A)$$The second city tax is $$8$$ more.$$0.08A+0.12(400-A)=28$$Simplify.$$0.08A+48-0.12A=28$$$$48-0.04A=28$$$$-0.04A=-20$$$$A=500$$This contradicts the fact that the two prices sum to $$400$$.So, no such value is possible.Final answer: $$\text{No such value}$$