I have a few questions within the same subject of Alg Thank

I have a few questions within the same subject of Alg. Thank you!

A goldsmith combined an alloy that costs $4.30 per ounce with an alloy that costs $1.80 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.35 per ounce?

Find the cost per ounce of a sunscreen made from 100 oz of a lotion that costs $2.50 per ounce and 150 oz of a lotion that costs $5.00 per ounce. (Round your answer to the nearest cent.)

A dentist invested a portion of $11,000 in a 8% annual simple interest account and the remainder in a 7.5% annual simple interest government bond. The two investments earn $860 in interest annually. How much was invested in each account?

Joseph Abruzzio is the manager of a trust. He invested 30% of a client\'s cash in government bonds that earn 6.5% annual simple interest, 30% in utility stocks that earn 7% annual simple interest, and the remainder in an account that earns 8% annual simple interest. The total annual interest earned from the investments was $5,365. Find the total amount invested.

Solution

1) A goldsmith combined an alloy that costs $4.30 per ounce with an alloy that costs $1.80 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.35 per ounce?

--- Let x ounce of alloy costing $ 4.30 ounce

--- Let y ounce of alloy costing $ 1.80 per ounce

x + y = 200 ----( 1)

4.3x + 1.8y = 470 ----(2)

------------------------------

Multiplying equ. (1) by 4.3:

4.3x + 4.3y = 860

4.3x + 1.8y = 470

------------------------( subtract)

2.5y = 390 ----> y = 156 ounce

x = 200 - 156 = 44 ounce

2) A dentist invested a portion of $11,000 in a 8% annual simple interest account and the remainder in a 7.5% annual simple interest government bond. The two investments earn $860 in interest annually. How much was invested in each account?

----- Let $x be invested at 8% simple interest

S.I. = x*8*1/100 = 0.08x

----- ( 11000 -x) be invested at 7.5%

S.I. = ( 11000 -x)*7.5*1/100 = 825 - 0.075x

Total interest = 0.08x + 825 -0.07x = 860

0.01x = 35

x = $3500 @ 8%

11000 -x = $ 7500