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Sergio [31]
3 years ago
9

Alexandra has some dimes and some quarters. She has no more than 21 coins worth a minimum of $3.75 combined. If Alexandra has 4

dimes, determine the minimum number of quarters that she could have. If there are no possible solutions, submit an empty answer.
Mathematics
1 answer:
olga55 [171]3 years ago
4 0

Answer:

A minimum of 10 dimes and 11 quarters is what Alexandra will have

Step-by-step explanation:

Let

d = number of dimes

q = number of quarters

Since she has 21 coins altogether,

d + q = 21------------------------equation 1    

  •  If these coins are worth $3.75 then

0.10 x d + 0.25 x q = 3.75

  • which is 0.10d +.25q =3.75 --------------------------equation 2

where $.10 is the value of one dime and $.25 is the value of one quarter

make d the subject of formula from equation 1 d = 21 -q----------equation 3

 insert it in equation 2

0.10d +0.25q =3.75

0.10(21-q) + 0.25q = 3.75

0.1(21)-0.1q+0.25q=3.75

2.1 +0.15q = 3.75

0.15q  = 3.75-2.1 = 1.65

q = 1.65/0.15 =165/15 =11

  • since we have the value of q insert in equation 3

d = 21 - q

d = 21-11

d = 10

Alexandra has 10 dimes and 11 quarters.

from my calculation i can see that the a minimum of 10 dimes and 11 quarters is what Alexandra will have

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34.3 in, 36.3 in

Step-by-step explanation:

From the question given above, the following data were obtained:

Hypothenus = 50 in

1st leg (L₁) = L

2nd leg (L₂) = 2 + L

Thus, we can obtain the value of L by using the pythagoras theory as follow:

Hypo² = L₁² + L₂²

50² = L² + (2 + L)²

2500 = L² + 4 + 4L + L²

2500 = 2L² + 4L + 4

Rearrange

2L² + 4L + 4 – 2500 = 0

2L² + 4L – 2496 = 0

Coefficient of L² (a) = 2

Coefficient of L (n) = 4

Constant (c) = –2496

L = –b ± √(b² – 4ac) / 2a

L = –4 ± √(4² – 4 × 2 × –2496) / 2 × 2

L = –4 ± √(16 + 19968) / 4

L = –4 ± √(19984) / 4

L = –4 ± 141.36 / 4

L = –4 + 141.36 / 4 or –4 – 141.36 / 4

L = 137.36/ 4 or –145.36 / 4

L = 34.3 or –36.3

Since measurement can not be negative, the value of L is 34.3 in

Finally, we shall determine the lengths of the legs of the right triangle. This is illustrated below:

1st leg (L₁) = L

L = 34.4

1st leg (L₁) = 34.3 in

2nd leg (L₂) = 2 + L

L = 34.4

2nd leg (L₂) = 2 + 34.3

2nd leg (L₂) = 36.3 in

Therefore, the lengths of the legs of the right triangle are 34.3 in, 36.3 in

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3 years ago
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