Substituting this value of y in (1), we have x+36=46 X= 46-3610 21. x+y=18 Add or subtract. x-y= 4 Answers. x = 10, y = 12. 22. 4x+3y=17 (1) Multiply (2) by 2 and subtract. 2xy= 1 (2) 23. 3x+4y=48 Add. x-4y= 0 24. 3x+5y=13 (1) Multiply (1) by 7 and (2) by 3. 7x+3y=13 (2) Subtract. 25. 4x+5y= 32 Add. 6x-5y=-2 26. 3x+4y=3 (1) Multiply (2) by 2. Add. 12x-2y=3 (2) 27. 5x=6y+5 Transpose. 3x=5y-4 28. 3x+5y+8=0 2xy-12=0 29. y-2x=8x-1 2y-4x=y+x+9 3. The product of the first of two numbers by 5, added to the product of the second by 3, gives 37. The product of the first by 6, diminished by 5 times the second, equals 10. Find the numbers. 4. Divide 65 into two parts whose difference shall be 19. (Let x and y parts. Solve also by one unknown quantity.) = 5. A person pays $103 with 32 bills, some of them $2 bills, the others $5 bills. How many of each does he use? 6. For 25 head of pigs and sheep, a farmer received $145. How many of each did he sell, if he sold the former at $7 each, the latter at $5 each? 7. 10 oranges and 4 peaches cost 38; 6 oranges and 7 peaches cost 32. Find the cost of an orange. Of a peach. 8. 5 pounds of tea and 3 pounds of coffee cost $3.75; 8 pounds of tea and 1 pound of coffee cost $5.05. What is each worth per pound? 9. A farmer buys a certain number of horses at $125 each, four times as many cows at $45 each, eight times as many sheep at $10 each, and half as many pigs at $5 each, spending $1,550 for all. How many of each does he buy? 10. A man paid 75¢ for 2 pounds of raisins and 3 pounds of cheese. 5 pounds of raisins and 2 pounds of cheese at the same price would have cost 944. What did each cost per pound? 11. The sum of two numbers is 19. The sum of the second number and ten times the first, minus the sum of the first and ten times the second, equals 45. What are the numbers? 12. Reduce to an equivalent fraction, the sum of whose numerator and denominator shall be 126. 13. What fraction equivalent to has 147 for the difference between its numerator and denominator? (x − y = − 147. Why?) 14. 10 pounds of coffee at 30¢ per pound are mixed with x pounds of coffee at 25¢ per pound. What is x equal to, when the mixture is worth 26¢ per pound? 25 x + (10 × 30) = 26 (10 + x). 15. A grocer mixes green tea costing 60 per pound with black tea costing 40 per pound. He uses 100 pounds in all, and the mixed tea costs him 48¢ per pound. How many pounds of each does he use? = Let x number of pounds of black tea; y = number of green. x+y= number of pounds of mixed tea. x + y = 100; 40x + 60 y = 48 (x + y). Then an equation containing only two unknown quantities. Compare the two equations (d) and (e), which contain the Substituting this value of y in (d), we have 110-14 z 12, 14z= — 98, z= = 7. Substituting values of y and z in (a), we have 3x+10-712, 3x=9, x = 3. Ans. x = 3, y = 5, 2= 7. 2. Find the values of the unknown quantities in the following equations: = x-3y+2z 3 (a) 2x+y+32=22 (b) 5x+2y+7z=51 (c) Multiply (a) by 2, and subtract from (b). Multiply (a) by 5, and subtract from (c). This gives two equations, each of which contains two unknown quantities. Compare these two resulting equations, and eliminate y. Eliminate z by comparing (a) and (b), multiplying the former by 5. Compare (a) and (c), multiplying the former by 2. |