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Art [367]
3 years ago
12

Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many of each kind of coin does she have?

Mathematics
1 answer:
VMariaS [17]3 years ago
8 0
Let's set up the equations we know.
Q+D=100, where Q=number of quarters, and D=number of dimes
.25Q + .1D = 21.40 (because a quarter is worth .25 and a dime worth .10)

Using the first equation, let's isolate one of our variables. I'll pick Q.
Q+D=100
Subtract D from each side
Q=100 - D

Now that we have this new equation, let's plug it into our second equation.
.25Q + .1D = 21.40
.25(100-D) + .1D = 21.40
Distribute the .25
25 - .25D + .1 D = 21.40
Combine like terms
25 - .15D = 21.40
Subtract 21.40 from each side
3.6 - .15D = 0
Add .15 D to each side
3.6 = .15D
Divide each side by .15
D = 24

Now that we have D, we can solve for Q
Q= 100 - D
= 100 - 24
Q = 76

Sue has 24 dimes and 76 quarters.

Let's check our work to make sure.
.25(76) + .1(24) = 
19 + 2.4 = 21.4 √
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Plz help me with this math and also explain
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Step-by-step explanation:

<h2>[1]</h2>

  • SI = $250
  • Rate (R) = 12\sf \dfrac{1}{2} %
  • Time (t) = 4 years

\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\

\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\

\longrightarrow \tt { 250 \times 100 = P \times 50} \\

\longrightarrow \tt { 25000 = P \times 50} \\

\longrightarrow \tt { \dfrac{25000}{50} = P } \\

\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\

Therefore principal is $500.

<h2>__________________</h2>

<h2>[2]</h2>

  • 2/7 of the balls are red.
  • 3/5 of the balls are blue.
  • Rest are yellow.
  • Number of yellow balls = 36

Let the total number of balls be x.

→ Red balls + Blue balls + Yellow balls = Total number of balls

\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\

\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\

\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\

\longrightarrow \tt{ 31x + 1260= 35x} \\

\longrightarrow \tt{ 1260= 35x-31x} \\

\longrightarrow \tt{ 1260= 4x} \\

\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\

\longrightarrow \underline{\boxed{  \tt { 315 = x }}} \\

Total number of balls is 315.

A/Q,

3/5 of the balls are blue.

\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\

\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\

\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\

\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\

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In parallelogram LMNO,NO=10.2 and LO=14.7 what is the perimeter of parallelogram LMNO?
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