Help me! Thanks a lot.

A jeweler wants to make 14 grams of an alloy that is precisely 75% gold.. The jeweler has alloys that are 25% gold, 50% gold, &a

Goryan [66]

Given that the jeweler has alloys that are 25% gold, 50% gold, and 82% gold.

As he wants to make 14 grams of an alloy by adding two different alloys that is precisely 75% gold, so one alloy must have a percentage of gold more than 75%.

One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

Case 1: 82% gold + 50% gold

Let x grams of 82% gold and y grams of 50% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 50% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times y \\\\$

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 50/100 \times (14-x)$ [as x+y=14]

$\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\$

$\Rightarrow x =(25 \times 14)/32=10.9375$ grams

and $y = 14-x= 14-10.9375=3.0625$ grams.

Hence, 10.9375 grams of 82% gold and 3.0625 grams of 50% gold added to make 14 grams of 75% gold.

Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\$

$\Rightarrow x =(50 \times 14)/57=12.28$ grams

and $y = 14-x= 14-12.28=1.72$ grams.

Hence, 12.28 grams of 82% gold and 1.72 grams of 50% gold added to make 14 grams of 75% gold.

3 0

2 years ago

Here is a rectangle which has a width of x cm. x cm

miskamm [114]

Answer:

278.25 cm2

Step-by-step explanation:

If the width of the rectangle is x (cm), as the length is 8cm longer, so that the length of the rectangle is: x + 8 (cm).

In the attached image, we can see the length of each side. Total length of the sides are 90 cm.

=> (x + x + 8) + x + 8 + (x+8) + (x + x + 8) + x + 8 + (x +8) = 90

=> 8x + 48 = 90

=> 8x = 90 - 48 = 42

=> x =42/8 = 5.25 (cm)

=> The width of the rectangle is 5.25cm

=> The length of the rectangle is: 5.25 + 8 = 13.25 cm

=> The area of one rectangle is: Length x Width = 5.25 x 13.25 = 69.5625 cm2

As the 8-sided shape is made from 4 rectangles, so that:

Area of 8 sided shape = 4 x Area of the rectangle = 4 x 69.5625 = 278.25 cm2

6 0

2 years ago

Simplify.... -5(8x+3)

Brut [27]

Answer:

-40x-15

You multiply using the distributive property.... Hope it helped :)

7 0

3 years ago

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Ble. 6 co 10 square units

Vlada [557]

Answer:

1/2×10×6=30

Step-by-step explanation:

H=6

L=10

therefore;

1/2×6×10=30

5 0

2 years ago

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Find the erea of the trapezoid. show work for brainliest

Alexandra [31]

Answer:

the area of the trapezoid is 32

Step-by-step explanation:

a (base)2

b (Base)6

h (height)8

6 0

2 years ago