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plz help me answer these questions i will mark you the brainiest
1) Gracie had some nickels and dimes in her purse totaling $1.65. She had 6 more dimes than nickels. How many coins of each type did she have?

2)Jimmy had $5.25 in nickels and quarters. If he had 15 more nickels than quarters, how many coins of each type did he have?

3)There were 180 students in attendance at the dance. If there were 32 more boys than girls at the dance, how many girls and boys were at the dance?

4)There were 293 tickets sold for a concert. Tickets purchased before the concert were $10, but tickets purchased at the gate were $15. The total ticket sales were $3495. How many people bought tickets before the concert, and how many purchased tickets at the gate?

Respuesta :

baglesrfine

Answer:

1. 7 Nickels, 13 Dimes

2. 30 Nickels, 15 Quarters

3. 74 Girls, 106 Boys

4. 180 tickets bought before and 113 bought at the gate

Step-by-step explanation:

mhanifa

Answer:

  • 1) 7 nickels and 13 dimes
  • 2) 15 quarters and 30 nickels
  • 3) 74 girls and 106 boys
  • 4) 180 tickets bought before, 113 - at the gate

Step-by-step explanation:

1)

Nickel: n = 5c, Dime: d = 10c

Equations as per given:

  • d = n + 6
  • 5n + 10d = 165c

Substitute d:

  • 5n + 10(n+6) = 165
  • 5n + 10n + 60 = 165
  • 15n = 105
  • n = 105/15 = 7
  • d = n+ 6 = 7 + 6 = 13

2)

Nickels: n = 5c, Quarters: q = 25c

Equations as per given:

  • n = q + 15
  • 5n + 25q = 525c

Substitute n:

  • 5(q + 15) + 25q = 525
  • 5q + 75 + 25q = 525
  • 30q = 450
  • q = 15
  • n = q + 15 = 15 + 15 = 30

3)

Boys = b

Girls = g

Equations as per given:

  • b + g = 180
  • b = g + 32

Substitute b:

  • g + 32 + g = 180
  • 2g = 148
  • g = 74
  • b = 74 + 32 = 106

4)

Tickets purchased at the gate: g = $15

Tickets purchased before the concert: b = $10

Equations as per given:

  • b + g = 293 ⇒ b = 293 - g
  • 10b + 15g = 3495

Substitute b:

  • 10(293 - g) + 15g = 3495
  • 2930 - 10g + 15g = 3495
  • 5g = 3495 - 2930
  • 5g = 565
  • g = 565/5
  • g = 113
  • b = 293 - g = 293 - 113 = 180

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