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Colt1911 [192]
4 years ago
12

What the equations are

Mathematics
1 answer:
strojnjashka [21]4 years ago
6 0
So, first lets define our variables: 
 
let x = the number of dimes
let y = the number of nickels

so our first equation would be x+y = 16

Since dimes are 10 cents and nickels are 5 cents the next equation would be as follows: 

.10x+.05y = 1.35

now change the first equation so y = -x+16
now substitute:

.10x+.05(-x+16) = 1.35
then multiply so you get .10x+-.05x+0.8=1.35

combine like terms and you get .05x+0.8 = 1.35
then subtract 0.8 from both sides and you get .05x = 0.55 then subtract
and you get x = 11 then substitute 11 for where x should be and you should get y = 5

So, you have 11 dimes and 5 nickels 
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What two partial products would you add to find 513 x 46
Afina-wow [57]
First, let me do the Mathematical part of that, and then I shall explain the theory behind it.

Mathematical part:
We are going to multiply 513 with 46. So the two partial products that we are going to choose are 40 and 6.

Multiply 513 with 6 first.

    513
    x46
--------------------------
      18 (as 6*3 = 18)
      60 (as 6*10 = 60; In 513, the digit at tenths place is 1, so 1*10=10)
  3000 (as 6*500 = 3000; In 513, 5 is at hundredth place, so 5*100=500)
    120 (as 40*3 = 120; since 4 is at the tenth place, so 4*10=40)
    400 (as 40*10 = 400)
20000 (as 40*500 = 20000)
--------------------------
23598 (Add all of them)


Theory:
As you can see above that we have chosen the two partial products individually which are 6 and 40. Since 4 in 46 is in tenth place, we have to consider it 40 (since 4*10 = 40). One by one, we first multiply 6 with 513. Then we move to the tenth place, and multiply 513 with 40. At the end, we have added all the results we found after multiplication.

Check: If we check the multiplication result by using the calculator, we would get the same result (23598).

Another Method (instant):
513 * (40+6) = (513*40) + (513*6) = 23598.
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