Question

1. darren and his two siblings ages are three consecutive odd numbers. if the sum of their ages is 51, what are the three ages? 6. melissa buys 2 1/2 pounds of salmon and 1 1/4 pounds of trout. she pays a total of $31.25, and the trout costs $0.20 per pound less than the salmon. what would be the combined cost of 1 pound of salmon and 1 pound of trout? a $15.60 b $15.80 c $16.60 d $16.80 7. terrell arranges x roses at $3.50 each with 10 carnations at $2.25 each. he makes a bouquet of flowers that averages $3.00 per flower. select the equation that models the situation. a 3.50x + 2.25(10)=3(x + 10) b 3.50x + 2.25 = 0.75x c 3.50x + 3 = 22.5(x + 10) d 3.50x + 2.50 = 0.75(x + 10)

Explanation:

Step1: Solve question 6

Let the cost per - pound of salmon be $x$ dollars. Then the cost per - pound of trout is $(x - 0.20)$ dollars.
Melissa buys $2\frac{1}{2}=\frac{5}{2}$ pounds of salmon and $1\frac{1}{4}=\frac{5}{4}$ pounds of trout.
The total cost equation is $\frac{5}{2}x+\frac{5}{4}(x - 0.20)=31.25$.
First, expand the equation: $\frac{5}{2}x+\frac{5}{4}x-\frac{5}{4}\times0.20 = 31.25$.
$\frac{5}{2}x+\frac{5}{4}x-0.25 = 31.25$.
Find a common denominator for the $x$ terms. The common denominator of 2 and 4 is 4. So, $\frac{10}{4}x+\frac{5}{4}x=31.25 + 0.25$.
$\frac{10x+5x}{4}=31.5$.
$\frac{15x}{4}=31.5$.
Multiply both sides by 4: $15x=31.5\times4 = 126$.
Divide both sides by 15: $x = 8.4$.
The cost per - pound of trout is $x-0.20=8.4 - 0.20 = 8.2$ dollars.
The combined cost of 1 pound of salmon and 1 pound of trout is $8.4+8.2=16.6$ dollars.

Step2: Solve question 7

The total cost of roses is $3.50x$ dollars (since each rose costs $3.50$ dollars and there are $x$ roses).
The total cost of carnations is $2.25\times10 = 22.5$ dollars (since there are 10 carnations and each costs $2.25$ dollars).
The total number of flowers is $(x + 10)$ flowers.
The average cost per flower is $3$ dollars, so the total cost of all the flowers is $3(x + 10)$ dollars.
The equation that models the situation is $3.50x+2.25\times10=3(x + 10)$.

Answer:

1. C. $16.60$
2. A. $3.50x + 2.25(10)=3(x + 10)$