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Alexandra [31]
3 years ago
11

Consider the following system of equations:

Mathematics
1 answer:
IrinaK [193]3 years ago
3 0

Answer:

x = 6 ; y = -9

Step-by-step explanation:

8 x + 2 y = 30  ..........equ No 1

7 x + 2 y = 24......... equ No 2

8 x = 30 - 2y

∴ x =\frac{ 30 - 2 y}{8}

substituting the value of x in equ No 2

7 \frac{30 - 2 y}{8} + 2 y = 24

7 ( 30 -2 y) + 2 y × 8 = 24 × 8

7 × 30 - 14 y + 16 y = 192

210 + 2 y = 192

2 y = 192 - 210

2 y = - 18

∴ y = - 9

put y = -9 , 8 x = 30 - 2 y

        8 x = 30 - 2 ( -9)

    8 x = 30 - ( -18)

  8 x = 48

∴ x = 6

x = 6 ; y = -9

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Gabby has a bag containing 36 nickels and quarters. The total value of the coins is $5. How many quarters does gabby have?
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There are 20 nickels and 16 quarters

<em><u>Solution:</u></em>

Let "n" be the number of nickels

Let "q" be the number of quarters

We know that,

1 nickel = 0.05 dollar

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Therefore,

n + q = 36

n = 36 - q ------- eqn 1

<em><u>The total value of the coins is $5</u></em>

<em><u>Thus we frame a equation as:</u></em>

number of nickels x 1 nickel + number of quarters x 1 quarter = 5

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0.05(36 - q) + 0.25q = 5

1.8 - 0.05q + 0.25q = 5

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q = 16

<em><u>Substitute q = 16 in eqn 1</u></em>

n = 36 - 16

n = 20

Thus there are 20 nickels and 16 quarters

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