Robin has a collection of nickels, dimes, and quarters worth $63.50. she has 30 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?

The first thing we must do is define variables:

x: number of nickels

y: number of dimes

z: number of quarters

We write the system of equations:

0.05x + 0.1y + 0.25z = 63.50

y = x + 30

z = 2y

Solving the system by substitution we have:

0.05x + 0.1 (x + 30) + 0.25 (2 (x + 30)) = 63.50

0.05x + 0.1x + 3 + 0.5x + 15 = 63.50

0.65x = 63.50 - 18

x = 45.5 / 0.65

x = 70

Then, the value of z and y is:

y = x + 30

y = 70 + 30

y = 100

On the other hand:

z = 2y

z = 2 (100)

z = 200

70 nickels

100 dimes

200 quarters

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

a

step-by-step explanation: