You have 14 coins that are nickles and quarters that equals 2 dollars how do you solve using substitution?

Question

You have 14 coins that are nickles and quarters that equals 2 dollars how do you solve using substitution?

in progress 0
Kaylee 8 hours 2021-09-14T02:49:59+00:00 1 Answer 0

Answers ( )

    0
    2021-09-14T02:51:05+00:00

    Answer:

    The question is incorrect but if half nickels and quarters exist then you could say the answer is 7.5 nickels and 6.5 quarters.

    The problem:

    14 coins that are either nickels are quarters

    The total dollar amount of these coins is 2 dollars

    Step-by-step explanation:

    Let n be the number of nickels.

    Let q be the number of quarters.

    We are given that n+q=14 and that .05n+.25q=2.

    I’m going to choose to solve the system by elimination.

    Multiplying the first equation by .25 gives:

    .25n+.25q=.25(14)

    .25n+.25q=3.5

    So let’s line the equations up now:

    .25n+.25q=3.5

    .05n+.25q=2

    ———————If we subtract the equations, the variable q will be eliminated.                Thus, we will able to solve for the variable n.

    .20n+0q=1.5

    .20n=1.5

    Dividing both sides by .2 gives:

    n=7.5

    If n=7.5 and n+q=14, then we have 7.5+q=14 by substitution property.

    We can subtract 7.5 on both sides giving us:

    q=14-7.5=6.5

    We cannot have 7.5 nickels and 6.5 quarters but this satisfies the given information.

    Check:

    7.5+6.5=(7+6)+(.5+.5)=13+1=14

    7.5(.05)+6.5(.25)=2

    Now, the requested way which is by substitution:

    Let n be the number of nickels.

    Let q be the number of quarters.

    We are given that n+q=14 and that .05n+.25q=2.

    We can solve the first equation for either n or q and then substitute that into the other equation allowing us to solve for the other variable.

    Let’s solve for q by subtraction n on both sides:

    q=14-n

    We are going to replace q in the second equation with (14-n) giving us:

    .05n+.25(14-n)=2

    Distribute:

    .05n+3.5-.25n=2

    Combine like terms:

    -0.2n+3.5=2

    Subtract 3.5 on both sides:

    -0.2n=-1.5

    Divide both sides by -0.2:

    n=7.5

    Since q=14-n and n=7.5, then q=14-7.5=6.5 .

    We are already check the solution above.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )