In 2013, Gold Prices Were Ridiculously High. This Is How It Changed Wedding Gifts.

Carats needed=10x22=220. Carats available in one gold coin=1x18=18. Carats available in one gold links=1.5x14 =21. So, we can see, 3 coins = 3x18 = 54 carats, 8 links = 8x21 = 168 carats. Total = 222 carats. Et voila..!!

Your sister needs 10 ounce, 22-karat gold, which means, $(10 oz) \times (\frac {22} {24})karat$ approximately equal to $9.17 oz-karat$ .

A coin equates to 1 ounce, 18-karat gold, which means, $(1 oz) \times (\frac {18} {24})karat$ = $0.75 oz-karat$ .

A link is 1.5 ounce, 14-karat gold = $0.875 oz-karat$ .

With these statements identified, let us choose for an answer that will satisfy the required value $9.17 oz-karat$ .

Starting from the rightmost choice, 6 coins and 5 links, gives us $(6 \times 0.75 oz-karat + 5 \times 0.875 oz-karat) = 8.88 oz-karat < 9.17 oz-karat$ , therefore this is not the answer.

Next is, 5 coins and 6 links, which gives us $(5 \times 0.75 oz-karat + 6 \times 0.875 oz-karat) = 9 oz-karat$ , still less than the required value. Still, this is not the answer.

Then we have, 4 coins and 7 links, which gives us $(4 \times 0.75 oz-karat + 7 \times 0.875 oz-karat) = 9.13 oz-karat$ , a very close value but is still not enough to satisfy what the sister wants.

Finally we have, 3 coins and 8 links which gives us $(3 \times 0.75 oz-karat + 8 \times 0.875 oz-karat) = \boxed{9.25 oz-karat} > 9.17 oz-karat$ , which means that this is more than enough to satisfy what the sister wants, therefore this is the answer.

First of all, carat is a unit that indicates purity (of gold ,here). And 24 carat indicates a 100% pure gold article. 18 carat means 18 units of gold mixed with 4 units of some other metal. Similarly for the 14 carat(14 & 8).

Now, 1 gold coin given by granny contains 18 parts of gold per ounce. 1 gold link given by mother contains 21 parts of gold per 1.5 ounce. ( since 1 ounce contains 14 parts gold)

So, ideal option can be found by the equation [( _ coins x 18) + ( _links x 21 )] parts of gold

Since we require 22 carat, 10 ounce necklace, that is, 22 x 10 = 220 parts of gold

so, melting 3 coins and 8 links, we get 221 parts of gold, which would be ideal for the sister's demands.

See the formulae to be used is ounce no. of carats no. of items Therefore 10 \times 22 \times 1=18 x+1.5 \times 14 y where x and y are respectively coins and links Put the values given in options and the one which is satisfies the equality or is greater than left hand side can be the answer. Thus on substituting option 1 we right hand value to 222 which is greater than 220 thus Option 1 is correct.

The Links Have More Gold Than The Coins.. as problem asks for enough gold and not exactly equal AND also only one Of the options is Correct With all having almost Same sum of number of gold coins and links... THE ONE WITH MOST NUMBER OF LINKS IS THE ANSWER

for this let coins units =X and links = Y then (X 1 14/22)+(Y 1.5 14/22)=10 Having solve it we can find answer - 3 coins and 8 links

Its all about product value, The product value of 1coin is 1 Ounce x 18 Carat = 18 O.C & value of Chain = 1.5 Ounce x 14 Carot = 21 O.C. So the option 3 Coins & 8 links = 222 O.C which is slightly higher than the req. i.e 10 Ounce x 22 Carot = 220 O.C. Then the option 3 Coins & 8 Links is correct.

24 carat is 100% gold . 10 ounce 22 carat -----> 22/24 X 10 = 9.166667 ounce pure gold

18/24 X1 = 0.75 ------> 1 coin has 0.75 ounce pure gold

14/24 X 1.5 = 0.875 -----> 1 link has 0.875 ounce pure gold

we see 3 X 0.75 + 8 X 0.875 = 9.25 is the only option greater than 9.166666 ounces

Good day ! :)

Let C be the no of gold coins and L be the no of links which will give sufficient amount of gold for the sister.

Then,(18/24) 1 C + (14/24) 1.5 L > (22/24)*10.

values of 3 and 8 for C and L satisfy this inequality.

No other answer satisfy this inequality.

x=no of coins y=no of links our required weight is 10 ounce x ((18/24)/(22/24)) * 1+y ((14/24)/(22/24)) * 1.5=10 x (18/22)+1.5 y*(14/22)=10 try iteration you will get x=3 and y=8

10 ounces of 22 carat = 220 carats in total (22*10). One coin (1 ounce and 18 carat ) = 18 carats ; one link 9 1.5 ounce and 14 carat ) = 21 carats . Multiply the no. of coins to the carats (18) and links to carats (21) so that it should be = or > 220 carats . I guess it happens with A to come 222 carats.

It is really simple. We need to multiply ounces by carats to get product not less than 220. Only the first option matches with this.

Actually, I believe that carat here should be spelled with a 'k', making it karat=unity of purity out of 24. With 22 karats the amount of gold ounces out of total would be 22\24 * 10 = 9.1667. It's easy to then see which option gives the correct combination to bring about that much gold.