Question

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

Answer 1

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:

`n+d+q=36` .....(1)

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

`n=2d-3` ....(2)

The total value of the coins is $5.20.

`0.10d+0.05n+0.25q=5.20` .... (3)

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

`2d-3+d+q=36`

=>
`3d+q=39` ....(4)

`0.10d+0.05(2d-3)+0.25q=5.20`

=>
`0.10d+0.10d-0.15+0.25q=5.20`

=>
`0.20d+0.25q=5.35` ...(5)

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

`0.75d+0.25q=9.75` now subtracting (5) from this we get;

`0.55d=4.4`

=> d = 8

Substituting d = 8 in
`3d+q=39`

`3(8)+q=39`

`24+q=39`

=> q = 15

Substituting values of d and q in
`n+d+q=36`, we get n

`n+8+15=36`

`n=36-23`

=> 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-(35x)/(100)=15.60`

=>
`(65x)/(100)=15.60`

=>
`65x=1560`

x = 24

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