Question

Janice has $2.30 made up of dimes, pennies and quarters. She has as many dimes as pennies and she has 17 coins in all. How many quarters does she have? (PLEASE HELP ME)

Answer 1

Answer:

7 quarters

Step-by-step explanation:

We can use the guess method.

17 coins altogether, and as many dimes as pennies.

The number of quarters must be odd. When you subtract an odd number of quarters from 17, you get an even number which will divide by 2 evenly giving you the same number of pennies and dimes.

Start with a guess of 7 quarters.

17 - 7 = 10

7 quarters + 5 pennies + 5 dimes have a value of $2.30

Wow, I got it with the first guess.

Answer: 7 quarters

Answer 2

Answer:The equation would be 230 = 25y + 10x + 1x or 230 = 25y + 11x

You would then need to solve for x and y, which I forget how to do with 2 variables but since we're working with small numbers what I would do is continuously subtract 25 from 230 until the remainder is divisible by 11.

230 - 25*7 = 55 = 11*5

x = 5

Ok, adding the equation 2x+y = 17 you will now be able to solve for the two variables using a system of equations.

yes, you can come up with an equation. actually, you can come up several equations to generate a system of equations.

your first equation is correct.

(1) 25q + 10d + 1p = 230

now, you're told that the number of dimes equals the number of pennies. that just means, in symbols:

(2) d = p

finally, you're told that you have 17 coins in all, i.e.:

(3) q + d + p = 17

you now have three equations and three unknowns. use (2) to reduce (1) and (3).

(1′) 25q + 11d = 230

(3′) q + 2d = 17

now solve for the three variables.