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Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs
$2.00 per pound while drought-resistant seed costs
$3.00 per pound. If for a particular day the two types of grass seed totaled
$68.00 and together weighed 25 pounds, how many pounds of bluegrass seed did Devin prepare?
Choose 1 answer:
(A) 4
(B) 7
(C) 18
(D) 21

Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs $\$ 2.00$ per pound while drought-resistant seed costs $\$ 3.00$ per pound. If for a particular day the two types of grass seed totaled $\$ 68.00$ and together weighed $25$ pounds, how many pounds of bluegrass seed did Devin prepare? $\newline$ Choose $1$ answer: $\newline$ (A) $4$ $\newline$ (B) $7$ $\newline$ (C) $18$ $\newline$ (D) $21$

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Experimental probability

Full solution

Q. Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs

\$ 2.00

per pound while drought-resistant seed costs

\$ 3.00

per pound. If for a particular day the two types of grass seed totaled

\$ 68.00

and together weighed

25

pounds, how many pounds of bluegrass seed did Devin prepare?

\newline

Choose

1

answer:

\newline

(A)

4

\newline

(B)

7

\newline

(C)

18

\newline

(D)

21

Cost and Weight Equations: Let's denote the number of pounds of bluegrass seed as $B$ and the number of pounds of drought-resistant seed as $D$ . We are given two pieces of information that we can turn into equations: $\newline$ $1$ . The total cost of the seeds is $\$68$ . $\newline$ $2$ . The total weight of the seeds is $25$ pounds. $\newline$ We can express these as two equations: $\newline$ $\$2.00 \times B + \$3.00 \times D = \$68.00$ (Equation $1$ : Cost equation) $\newline$ $B + D = 25$ pounds (Equation $2$ : Weight equation) $\newline$ We can use these equations to solve for $B$ and $D$ .
Solving for D: First, let's solve Equation $2$ for one of the variables. We can solve for D in terms of B: $\newline$ $D = 25 - B$ $\newline$ Now we have an expression for D that we can substitute into Equation $1$ .
Substituting into Equation $1$ : Substituting $D = 25 - B$ into Equation $1$ gives us: $\newline$ $\$2.00 \times B + \$3.00 \times (25 - B) = \$68.00$ $\newline$ Now we can distribute the $\$3.00$ into the parentheses and simplify the equation.
Distributing and Simplifying: After distributing we get: $\newline$ $2.00 \times B + 75.00 - 3.00 \times B = 68.00$ $\newline$ Now we combine like terms by subtracting $2.00 \times B$ from $3.00 \times B$ .
Combining Like Terms: This simplifies to: $\newline$ $-1.00 \times B + 75.00 = 68.00$ $\newline$ Now we can isolate $B$ by subtracting $75.00$ from both sides of the equation.
Isolating B: After subtracting we get: $\newline$ $-1.00 \times B = 68.00 - 75.00$ $\newline$ $-1.00 \times B = -7.00$ $\newline$ Now we can solve for B by dividing both sides by $-1.00$ .
Solving for B: Dividing by $-\$1.00$ gives us: $\newline$ $B = \frac{\$7.00}{-\$1.00}$ $\newline$ $B = -7$ $\newline$ However, we cannot have a negative number of pounds of seed, so there must be a mistake in our calculations.

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