Abby has 49 coins, consisting only of dimes and quarters, worth $8.35. How many dimes and how many quarters does she have?

1 answer:

4 0

Let q represent the number of quarters Abby has. Then the number of dimes she has is 49-q. The total amount of money she has in dimes and quarters is ...

25q +10(49 -q) = 835

15q + 490 = 835 . . . . . . simplify

q = (835 -490)/15 = 23 . . . . solve for q

Abby has 23 quarters and 26 dimes.

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Solve the following systems: 3x+4y=0 2x+3y=1

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Answer:

Answer is x= -4 and y= 3

Step-by-step explanation:

$given \: equations \: are \\ 3x + 4y = 0 \: \: and \: 2x + 3y = 1 \\ multiply \: by \: 2 \: in \: first \: equation \\ 6x + 8y = 0 \\ multiply \: by \: 3 \: in \: second \: equation \\ 6x + 9y = 3 \\ subtracting \: the \: above \: mentioned \: equation \: \\ we \: get \: - y = - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 3 \\ substitute \: y = 3 \: in \: first \: equation \\ 3x + 4(3) = 0 \\ 3x = - 12 \\ x = - 4$