Question

name:
algebra 1
3.6 quiz: problem solving using charts
solve the problems.

1. a flower shop sells bouquets of red and blue flowers. the bouquets of blue flowers have eighteen flowers in them. the bouquets with red flowers have fifteen flowers in them. there are five more bouquets of red flowers than there are blue flowers. the shop has a total of 1,065 red and blue flowers. find how many red flowers the shop has.
2. the length of rectangle a is 25 feet more than its width. rectangle b has a perimeter of 80 feet, and it is 3 feet wider and 2 feet longer than rectangle a. find the area of rectangle a and rectangle b.
3. a 10 - foot wide rectangular pool is 6 - feet longer than a rectangular 12 - feet wide patio. the perimeter of both the pool and patio together is 112 feet. what is the volume of the pool if the pool is 5 - feet deep?
4. tim went hunting in two locations. he shot 12 less ducks than his friend alex. if two - thirds of tim’s ducks were from location 1 and alex got a total of 48 ducks, how many ducks did tim shoot in location 2?
5. a school sold 475 tickets for a play. student tickets cost $2 and non - student tickets were $5. three - fifths of the tickets sold were non - student tickets and a total of $1,805 were earned from ticket sales. what was the earnings from just the student tickets?

Explanation:

1.

Step1: Let the number of blue - flower bouquets be $x$.

The number of red - flower bouquets is $x + 5$.

Step2: Set up an equation based on the total number of flowers.

The number of blue flowers is $18x$, and the number of red flowers is $15(x + 5)$. The total number of flowers is $18x+15(x + 5)=1065$.

Step3: Expand and simplify the equation.

$18x+15x+75 = 1065$. Combine like - terms: $33x+75 = 1065$.

Step4: Solve for $x$.

Subtract 75 from both sides: $33x=1065 - 75=990$. Then $x=\frac{990}{33}=30$.

Step5: Find the number of red flowers.

The number of red - flower bouquets is $x + 5=30 + 5 = 35$. The number of red flowers is $15\times35 = 525$.

Step1: Let the width of rectangle A be $w$.

The length of rectangle A is $l=w + 25$.

Step2: Find the dimensions of rectangle B.

The width of rectangle B is $w+3$, and the length of rectangle B is $(w + 25)+2=w + 27$.

Step3: Use the perimeter formula for rectangle B.

The perimeter of rectangle B is $P = 2((w + 3)+(w + 27))=80$. Simplify the equation: $2(2w+30)=80$.

Step4: Solve for $w$.

$4w+60 = 80$. Subtract 60 from both sides: $4w=20$, so $w = 5$.

Step5: Find the dimensions and areas of rectangles A and B.

For rectangle A, $l=w + 25=30$, and the area of rectangle A is $A_A=l\times w=30\times5 = 150$ square feet.
For rectangle B, $l=w + 27=32$, $w=w + 3=8$, and the area of rectangle B is $A_B=32\times8 = 256$ square feet.

Step1: Let the length of the patio be $x$ feet.

The length of the pool is $x + 6$ feet.

Step2: Use the perimeter formula for the pool and patio.

The perimeter of the pool is $P_{pool}=2(10+(x + 6))=2x+32$. The perimeter of the patio is $P_{patio}=2(12 + x)=2x+24$.

Step3: Set up an equation for the total perimeter.

$(2x+32)+(2x+24)=112$. Combine like - terms: $4x+56 = 112$.

Step4: Solve for $x$.

Subtract 56 from both sides: $4x=56$, so $x = 14$.

Step5: Find the length of the pool and its volume.

The length of the pool is $x + 6=20$ feet. The volume of the pool is $V=10\times20\times5=1000$ cubic feet.

Answer:

525

2.