A goldsmith has two alloys of gold, the first having a purity of 53% and the second having a purity of 83%. If x grams of the first alloy are mixed with y grams of the second, obtaining 100 grams of an alloy which contains 72.5% gold, find x to the nearest gram.

Correct  x = 35 grams  and y = 65 grams

Step-by-step explanation:

Given:

53%  purity of the first alloy

83%  purity of the second alloy

x = ?   mass of the first alloy

y = ?   mass of the second alloy

x + y = 100 grams  the mass of the mixture

72.5%   purity of the mixture

We can solve the problem by setting up a two system of equations:

First:                                            Second:

53 x + 83 y = 100 · 72.5              x + y = 100

x + y = 100                                   x : y = (83 - 72.5) : (72.5 - 53)

First system:

y = 100 - x  

From the second, we express y as a function of x and replace in the first

and get:

53 x + 83 (100 - x) = 7,250

53 x + 8,300 - 83 x = 7,250

30 x = 1050  ⇒ x = 1050 / 30 = 35 grams

x = 35 grams

y = 100 - 35 = 65 grams

y = 65 grams

Second system:

x + y = 100  

x : y = (83 - 72.5) : (72.5 - 53) = 10.5 : 19.5 = 105 : 195 = 7 : 13

x : y = 7 : 13  ⇒ x = (7/13) y

From the second, we express x as a function of y and replace in the first

and get:

(7/13) y + y = 100 / ·(13) ⇒ 7 y + 13 y = 1300 ⇒ 20 y = 1300

y = 1300 / 20 = 65 grams

y = 65 grams

x + 65 = 100  ⇒ x = 100 - 65 = 35 grams

x = 35 grams

God is with you!!!

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !

75

step-by-step explanation: