Easy Ten Points two word problems?

Question

1)A college graduate made 28,000 in her first year working. She invested half the money in two CDs that earned 3% and 5% annual interest. After one year she earned 625 in interest. How much was invested in the 3% account?

2)A 5×7 photograph has a rectangular cardboard mat frame that is an equal depth on all four sides. If the total area of the mat is 99 in^2, what is the depth of the mat?

Answer 1

1) X * 3% = 625

so, X = 12,500

2) (5 + a)*(7 + a) = 99

or, a^2 + 12a + 35 = 99

or, a^2 + 12a - 64 = 0

or, (a + 16)(a -4) = 0

since a cannot be negative, a = 4

depth of the mat is 4 in

Answer 2

Hi,

1)A college graduate made 28,000 in her first year working. She invested half the money in two CDs that earned 3% and 5% annual interest. After one year she earned 625 in interest. How much was invested in the 3% account?

x + y = 28000

.03x + .05y = 625

There is a problem with your information, for if the entire $28,000 was invested at only 3%, the interest would be $840, far more interest than you indicated was received.

Please check your numbers and revise.

2)A 5×7 photograph has a rectangular cardboard mat frame that is an equal depth on all four sides. If the total area of the mat is 99 in^2, what is the depth of the mat?

(2x + 5)(2x + 7) = 99

4x² + 24x + 35 = 99

4x² + 24x - 64 = 0

4(x² + 6x - 16) = 0

4(x + 8)(x - 2) = 0

x + 8 = 0

x = -8 The mat can't be -8" wide, so discard this answer.

x - 2 = 0

x = 2

The mat was 2" wide on each side. <==ANSWER

I hope that helps!! :-)