Mary has nickels and dimes totaling $1.00. If she has 14 coins, how many nickel and dimes does she have? ( )

Transcription

1 Math 60 Unit 7.4 Supplement Word Problems Using Two Variables Using two equations can make solving word problems easier. You may remember using one variable in a problem similar to this: Example 1: Mary has nickels and dimes totaling $1.00. If she has 14 coins, how many nickel and dimes does she have? If we set the number of dimes equal to x, the number of nickels she has is her total number of coins minus the nickels, or 14-x. our equation is then: Another way of solving this problem is by using two variables and two equations. Let the number of dimes and the number of nickels. Set up two equations, one involving number of coins, and the other involving value of coins. Multiply by -5 Substituting 6 for d:.

2 Example 2: The sum of two numbers is 50. One number is 5 less than 4 times the other number. Set up two equations: Their sum is 50 One number is 5 less than 4 times the other. Substituting: Substituting 11 for y: The two numbers are 11 and 39. Example 3: The sum of two numbers is 12 and one of the numbers is 4 more than the other. Find the numbers. Set up the two equations: Their sum is 12 The equations are: Substituting: One number is 4 more than the other Substituting 4 for x: The numbers are: 4 and 8. Problems involving mixing different solutions are basically set up similar to coin problems.

3 Example 4: A gourmet coffee shop has two different types of coffee. Type A costs $5.95 per pound and Type B costs $7.00 per pound. A customer wishes to purchase a mixture of these, using two times more of Type A than Type B. If the total cost for the customer is $56.70, how many pounds of each did the customer buy? the number of pounds purchased of Type A the number of pounds purchased of Type B 6 pounds of Type A and 3 pounds of Type B Example 5: The Be kind to Animals Pet Shop has two grades of dog food. One grade sells for 72 cents per pound and the other sells for 52 cents per pound. How many pounds of each must be used to produce 600 pounds of mixture selling for 60 cents per pound? number of pounds of first grade number of pounds of second grade Multiply by pounds 360 pounds

4 Example 6: A woman invested $50,000, part at 6% and part at 7%. Her yearly income is $3,200. Find the amount invested at each rate. amount invested at 6% amount invested at 7% Set up two equations: One involving money invested at each rate and one involving % of money invested multiply by -6 Substituting 20,000 for y: $30,000 invested at 6% $20,000 invested at 7%

5 Problems: 1. The sum of two numbers is 50. One number is 4 times the other. Find the numbers. 2. One number is 3 more than twice another. Their sum is 24. Find the numbers. 3. The sum of two numbers is 18. One number subtracted from the other is 6. Find the numbers. 4. The sum of two numbers is 72. One number is 8 more than the other. Find the numbers. 5. One number is 9 more than another. If the larger is increased by 7, the result is 5 times the smaller. Find the numbers. 6. One number is 3 less than another. If the larger is decreased by twice the smaller, the result is - 7. Find the numbers. 7. The sum of two numbers is 22. One number is 2 more than three times the other. Find the numbers. 8. One number is 9 less than twice another. The sum of the numbers is 12. Find the numbers. 9. One number is 4 more than another. If twice the smaller is added to the larger, the result is 28. Find the numbers. 10. One number is 2 less than another. If twice the larger is decreased by 3 times the smaller, the result is -10. Find the numbers. 11. A sum of money amounting to $5.20 consists of quarters and dimes. If there are 31 coins in all, how many of each kind are there? 12. A man has $10.40 in change consisting of 3 times as many quarters as nickels. How many quarters and nickels does he have? 13. A man has $4.30 in change consisting of 8 more nickels than quarters. How many quarters and nickels does he have? 14. A man has $355 in ten-dollar and five-dollar bills. There are ten more ten-dollar bills than fivedollar bills. How many of each kind does he have? 15. Admission fees at a football game were $1.25 for adults and $0.55 for children. The receipts were $ for 454 paid admissions. How many adults and children attended the game? 16. Admission fees at a professional football game were $7 for reserved seat and $4 for general admission. The total receipts for the game were $325,000 for 61,000 people. How many reserved seat and general admission tickets were sold? 17. A sum of $46,000 is invested, part in a small business which yields a 20% return each year and part in mutual funds which yield an 8% return each year. Find the amount invested at each rate if the yearly income from the two investments is $5, A trust fund containing $30,000 has been established for you. Part of the money is invested in a bank at a rate, while the rest is in a stock yielding a 7% rate. If you receive $1,830 a year from the two investments, find the amount invested at each different rate. 19. A sum of $3,000 is invested. Part at 5% and the remainder at 6%. Find the amount invested at each rate if the yearly income from the two investments is $ A woman has twice as much money invested at as he invested at 7%. If her yearly income from the investments is $300, how much does he have invested at each rate? 21. A man has three times as much money invested at 4% as he has invested at. If his yearly income from his investments is $268, how much does he have invested at each rate?

6 22. Yolanda spent $30.60 for walnuts and pecans. The walnuts cost $2.80 per pound and the pecans cost $3.20 per pound. If she has a total of 10 pounds of nuts, how many pounds of each does she have? 23. The Thrifty Coffee Shop blends coffee worth $3.00 per pound with coffee worth $4.25 per pound for a blend worth $3.50. The weight of $4.25 per pound coffee was of the weight of the $3.00 per pound coffee. How many pounds of each was used to make a mixture with a total value of $140? 24. For a party the hostess purchased party mix nuts for $5.70 per pound and some cereal mix for $2.20 per pound. If she wanted 5 pounds of the mixture worth $3.60 per pound, how many pounds of each did she purchase? 25. A confectioner has $4.00 per pound candy and $6.00 per pound candy. If she has a total of 16 pounds mixture worth $4.75 per pound, how many pounds of each were used to make the mixture? 26. The sum of $3800 was invested, part at 8% and part at 10%. If the yearly income from the 10% investment was $92 more than the income from the 8% investment, how much was invested at each rate?

7 Answers: , 14 quarters and 17 dimes. 12., 13 nickels and 39 quarters nickels and 13 quarters $5 bills and 27 $10 bills adults and 53 children ,000 reserved and 34,000 general 17. $16000 at 20% and $30,000 at 8% 18. $18000 at 5.5% and $12,000 at 7% 19. $1,100 at 5% and $1,900 at 6% 20. $3,000 at 6.5% and $1,500 at 7% 21. $4,800 at 4% and $1,600 at 4.75% pounds of walnuts and 6.5 pounds of pecans pounds and 16 pounds pounds and 3 pounds pounds and 6 pounds 26. $1600 and $2200