Gabe has 60 coins consisting of quarters and dimes. The combined value of the coins is $9.45. How many quarters and dimes does Gabe have?

There are 23 quarters and 37 dimes in the collection

Step-by-step explanation:

Let's name the two unknowns we need to find :

Q = number of quarters in the collection

D = number of dimes in the collection

So our first equation on the number of coins we have in the collection can be written as:

Q + D = 60

Now let's write an equation that takes care of the total value of the collection ($ 9.45), having in mind that each quarter is worth $ 0.25, and each dime is $ 0.10:

So let's solve this system of linear equations in "Q" and "D" by substitution. We use the first equation to solve for "d" for example, and then use this to substitute for D in the second equation:

Then, there are 23 quarters in the collection. We can find the number of dimes via the substitution equation we used:

your answer would be 12

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.