Abby has a collection of 61 dimes and nickels worth $4.40. how many nickels does she have? show steps

  34 nickels

Step-by-step explanation:

First, consider the value if they were all dimes. That would be 61×$0.10 = $6.10. Next, realize this is more than the actual amount by 1.70. Of course, replacing one of the 61 dimes by a nickel reduces the total amount by $.05, so we must have ...

  $1.70/$0.05 = 34

nickels in the mix.

Abby has 34 nickels.

Alternate solution methods

I like to solve these using number sense, as above. Equivalently, an equation can be written using n to represent the number of nickels. The total value is then ...

  .05n + .10(61 -n) = 4.40

  -.05n +6.10 = 4.40 . . . . . . eliminate parentheses

  -.05n = -1.70 . . . . . . . . . . . subtract 6.10

  n = -1.70/-.05 = 34

Hopefully, you notice some similarities between this solution and the one in words, above.

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Often, you will see this sort of problem formulated using two equations.

  n + d = 61 . . . . . . . . . . number of coins (d=#of dimes)

  .05n +.10d = 4.40 . . . .value of coins

If we solve this by substitution, we can use d=61-n, and get ...

  .05n +.10(61-n) = 4.40 . . . . . . looks like our equation in the previous section

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!