## anonymous 5 years ago Linda invests $13,000 for one year. Part is invested at 4%, another part at 5%, and the rest at 7%. The total income from all 3 investments is$705. The combined income from the 4% and 5% investments is $75 more than the income from the 7% investment. Find the amount invested at each rate. • This Question is Closed 1. anonymous x*0.04+y*0.05+(13000-x-y)*0.07=705 x*0.04+y*0.05-(13000-x-y)*0.07=75 solve for x and y 2. anonymous theres no z to it? 3. anonymous im so lost... 4. anonymous no there is no need 5. anonymous as z=13000-x-y 6. anonymous i still dont understand how to solve it... 7. anonymous let money invested for 4% be x let money invested for 5% be y so money invested for 7% is money left i.e 13000-x-y 8. anonymous ok..... 9. anonymous now total income is the sum of income from all so it's 1 eq now use second condition 10. anonymous ugh... im never gonna get this... 11. anonymous try it i will help u to get it never lose hope always try and u will get it 12. anonymous ok let me try, give me a few 13. anonymous im not gettin it because whatever I have it is cancellin x and y 14. anonymous so I cant solve for neither 15. anonymous have u solved 2 eq which i gave u? 16. anonymous ok i made a mistake, I got x=-13000, and y=9250 17. anonymous an z=16750 which are all probably wrong 18. anonymous k iet me check again 19. anonymous ok 20. anonymous (1)-(2) will give u value of z i.e 5571.4285.. 21. anonymous now solve others 22. anonymous ok now u lost me... 23. anonymous can somebody please help me solve this problem... 24. anonymous Interest Rate * Amount Loaned = return or return on interest or revenue Borrowing from Jas's work we have the following: Let x = amount loaned at 4% or 4/100 Note: 4/100 is 4% converted to a fraction. Let y = amount loaned at 5% or 5/100 The remaining cash is loaned at 7% or 7/100 The total income from all 3 investments is$705.$\left(\frac{4}{100}x\right)+\left(\frac{4}{100}y\right)+\left(\frac{7}{100}(13000-(x+y))\right)=705$ Solve the above equation for y now; we will need it later. Multiply through by 100, gather all of the y terms and put them on the left hand side and all of the other terms on the right hand side and then simplify. $y= \frac{1}{2} (20500-3 x)$ The combined income from the 4% and 5% investments is \$75 more than the income from the 7% investment. Since the left hand side is 75 more than the right, we add in an additional 75 to the right hand side to make both sides equal to each other. $\left(\frac{4}{100}x\right)+\left(\frac{5}{100}y\right)\text{= }75+\frac{7}{100} (13000-(x+y))$ Solve for y. $y= \frac{1}{12} (98500-11 x)$ Set the right hand sides of the y= equations above to each other as follows: $\frac{1}{2} (20500-3 x)\text{=}\frac{1}{12} (98500-11 x)$ and solve for x. $x=3500, y=\frac{1}{12} (98500-11*3500)=4500, 13000-3500-4500 =5000\text{ }$

25. anonymous

There is an error in the first equation expression. $\left(\frac{4}{100}y\right)\text{ should be changed t}\text{o }\left(\frac{5}{100}y\right)$ The computations were used with the latter.

26. anonymous

this is the same as i answered earlier

27. anonymous

Jas, The reason I put forth a solution was because after all of yesterday's back and forth on this problem, hermommy1101 in the last problem posting yesterday, issued a plea, "can somebody please help me solve this problem..." Just trying to help out.