Carter has 37 coins, all nickels and dimes in his piggy bank. the value of the coins is $3.10. how many dimes does carter have have. use substitution or elimination method

Carter has 25 dimes

Solution:

Let "n" be the number of nickels

Let "d" be the number of dimes

Given that Carter has 37 coins, all nickels and dimes in his piggy bank

number of nickels + number of dimes = 37

n + d = 37 -------- eqn 1

Given that value of coins is $ 3.10

Also, value of nickel is 0.05 dollar and value of dime is 0.10 (in dollars) and total value of these 37 coins is 3.10, so we can write:

number of nickels x value of 1 nickel + number of dimes x value of 1 dime = 3.10

0.05n + 0.10d = 3.10 ------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "n" and "d"

From eqn 1,

n = 37 - d ---- eqn 3

Substitute eqn 3 in eqn 2

0.05(37 - d) + 0.10d = 3.10

1.85 - 0.05d + 0.10d = 3.10

0.05d = 3.10 - 1.85

0.05d = 1.25

Thus carter has 25 dimes

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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