John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, $d$ $d$ , in his pocket.?

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John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, $d$ $d$ , in his pocket.?

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Answer 1 · 2018-05-01T04:32:48

$n = 4 + d$ $n = 4 + d$
$n + 2 d = 25$ $n + 2d = 25$

$d = 7$ $d = 7$

Explanation:

In this case, you would not write an equation, you would write two equations. This will give you a system with two equations and two unknowns. The equations will be linearly independent, meaning you'll be able to use them to solve for $d$ $d$ .

First, we know that John has four more nickels than dimes. Let $n$ $n$ be the number of nickels and $d$ $d$ the number of dimes. Then $n = 4 + d$ $n = 4+d$ represents the relative amounts of nickels and dimes.

Additionally, we know that our change totals $$ 1.25$ $$1.25$ . Since dimes are worth 10 cents and nickels worth 5, this can be modeled with the equation $0.05 n + 0.1 d = 1.25$ $0.05n + 0.1d = 1.25$ . To eliminate the decimals, we can multiply this through by 20 to yield $n + 2 d = 25$ $n + 2d = 25$ .

We then have the two equations:
$n = 4 + d$ $n = 4 + d$
$n + 2 d = 25$ $n + 2d = 25$

We will substitute the first into the second, giving
$n + 2 d = 25 \to (4 + d) + 2 d = 25 \to 3 d = 21 \to d = 7$ $n + 2d = 25 -> (4+d) + 2d = 25 -> 3d = 21 -> d = 7$ .

This gives us our answer; we have $7$ $7$ dimes. (Plugging this value of $d$ $d$ into the first equation also reveals that we have $11$ $11$ nickels.)

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John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, $d$ $d$ , in his pocket.?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, dd, in his pocket.?

1 Answer

Explanation:

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John has four more nickels than dimes in his pocket for a total of $1.25. How do you write an equation one could use to determine the number of dimes, $d$ $d$ , in his pocket.?