# Thread: 2 Word Problems, Alg 2, Please Help( Reply by 10am plz)

1. ## 2 Word Problems, Alg 2, Please Help( Reply by 10pm plz)

1) Ashley won $5000 in a contest. She invested some of the money at 5% simple interest and$400 less than twice that amount at 6.5%. In one year, she earned $298 in interest. How much did she invest at each rate? Formula = use table with Principle, Rate and Interest. Problem : Please assist with setting up the problem. I've tried but failed to solve it. The Answer in the book should be =$1800 at 5%; %3200 at 6.5%

2) Vincente and Ricarda have invested $27,000 in bonds paying 7%. How much additional money should they invest in a certificate of deposit paying 4% simple interest so that the total return on the two investment will be 6%? Formula = the same. Problem : the same. Answer :$13,500

2. Originally Posted by chamroeneng
1) Ashley won $5000 in a contest. She invested some of the money at 5% simple interest and$400 less than twice that amount at 6.5%. In one year, she earned $298 in interest. How much did she invest at each rate? Formula = use table with Principle, Rate and Interest. Problem : Please assist with setting up the problem. I've tried but failed to solve it. The Answer in the book should be =$1800 at 5%; %3200 at 6.5%
Let x be the amount invested at 5% interest. Then the other amount invested is (2x - 400)

the interest gained at 5% is 0.05x using the simple interest formula.

similarly, the interest gained at 6.5% is 0.065(2x - 400)

the total interest gained is 298. thus:

0.05x + 0.065(2x - 400) = 298

solve for x and you can complete the problem

3. Originally Posted by chamroeneng
2) Vincente and Ricarda have invested $27,000 in bonds paying 7%. How much additional money should they invest in a certificate of deposit paying 4% simple interest so that the total return on the two investment will be 6%? Formula = the same. Problem : the same. Answer :$13,500
Let x be the additional amount invested at 4%

So in total, we invested (27000 + x).

now, the interest gained by the 27000 is 0.07*27000

the interest gained by x is 0.04x

we want the return to be 6% of the total amount invested. meaning, we want the interest to be 0.06(27000 + x). thus:

0.07*27000 + 0.04x = 0.06(27000 + x)

now solve for x and that's your answer