Question

1. the sum of two numbers is 43. the larger number is 7 more than twice the smaller. find the smaller number.
2. ms. daisy and ms. rose decide to spruce up their gardens and go shopping at the same plant store. ms. daisy spends $177 on 3 rose bushes and 13 tulips. ms. rose spends $247 for 13 rose bushes and 13 tulips. find the cost of one rose bush.
3. opening night of the musical at finn’s school sells 52 child tickets and 13 adult tickets for a total of $767. on the second night, the musical sold 40 child tickets and 16 adult tickets for a total of $668. find the cost of a child ticket.
4. justin timberlake needs new microphones and speakers for his next concert. for a total of $291, he can buy 6 speakers and 3 microphones. if he buys 9 speakers and 11 microphones then the total is $586. find the cost of one microphone.

Explanation:

Problem 5

Step1: Define variables

Let $x$ = smaller number, $y$ = larger number.

Step2: Set up equations

$x + y = 43$; $y = 2x + 7$

Step3: Substitute $y$ into first equation

$x + (2x + 7) = 43$

Step4: Simplify and solve for $x$

$3x + 7 = 43$
$3x = 43 - 7 = 36$
$x = \frac{36}{3} = 12$

Step1: Define variables

Let $r$ = cost of rose bush, $t$ = cost of tulip.

Step2: Set up equations

$3r + 13t = 177$; $13r + 13t = 247$

Step3: Subtract first equation from second

$(13r + 13t) - (3r + 13t) = 247 - 177$

Step4: Simplify and solve for $r$

$10r = 70$
$r = \frac{70}{10} = 7$

Step1: Define variables

Let $c$ = cost of child ticket, $a$ = cost of adult ticket.

Step2: Set up equations

$52c + 13a = 767$; $40c + 16a = 668$

Step3: Simplify first equation

Divide by 13: $4c + a = 59$ → $a = 59 - 4c$

Step4: Substitute $a$ into second equation

$40c + 16(59 - 4c) = 668$

Step5: Simplify and solve for $c$

$40c + 944 - 64c = 668$
$-24c = 668 - 944 = -276$
$c = \frac{-276}{-24} = 11.5$

Answer:

12

---

Problem 6