Caps hock guess and check (or use algebra) to solve #3 & # 4 3. plato has 36 coins in nickels, dimes, and quarters. the number of nickels is three less than twice the number of dimes. the total value of the coins is $5.20. how many of each type of coin does plato have? mel 36 coinsin d
4. katy bought a ski hat that was marked down 35% to $15.60. what was the price of the hat before the markdown? (hint: she was in oregon where they do not have sales tax). 35 9. douon 15.60 5. sele amo ont 621.06

Part 1:

Let the nickels be = n

Let the dimes be = d

Let the quarters be = q

Plato has 36 coins in nickels, dimes, and quarters. So, equation forms:

   .....(1)

The number of nickels is three less than twice the number of dimes.

   ....(2)

The total value of the coins is $5.20.

  .... (3)

Substituting n=2d-3 in (1) and (3)

=>    ....(4)

=>

=>    ...(5)

Multiplying (4) by 0.25 and subtracting (5) from (4)

now subtracting (5) from this we get;

=> d = 8

Substituting d = 8 in

=> q = 15

Substituting values of d and q in , we get n

=> n = 13

Therefore Plato has 13 nickels, 15 quarters and 8 dimes.

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Part 2:

Let the original price of the ski hat be = x

Original price was marked down by 35% means value was lowered by 35%.

So, we can calculate as:

=>

=>

x = 24

Hence, the original price was $24 but after 35% marking down, it was available for $15.60.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.