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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 \$ 2.00 per pound while drought-resistant seed costs $3.00 \$ 3.00 per pound. If for a particular day the two types of grass seed totaled $68.00 \$ 68.00 and together weighed 2525 pounds, how many pounds of bluegrass seed did Devin prepare?\newlineChoose 11 answer:\newline(A) 44\newline(B) 77\newline(C) 1818\newline(D) 2121

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Q. Devin is a landscaper who needs to prepare different types of grass seed for his customers' yards. Bluegrass seed costs $2.00 \$ 2.00 per pound while drought-resistant seed costs $3.00 \$ 3.00 per pound. If for a particular day the two types of grass seed totaled $68.00 \$ 68.00 and together weighed 2525 pounds, how many pounds of bluegrass seed did Devin prepare?\newlineChoose 11 answer:\newline(A) 44\newline(B) 77\newline(C) 1818\newline(D) 2121
  1. Cost and Weight Equations: Let's denote the number of pounds of bluegrass seed as BB and the number of pounds of drought-resistant seed as DD. We are given two pieces of information that we can turn into equations:\newline11. The total cost of the seeds is $68\$68.\newline22. The total weight of the seeds is 2525 pounds.\newlineWe can express these as two equations:\newline$2.00×B+$3.00×D=$68.00\$2.00 \times B + \$3.00 \times D = \$68.00 (Equation 11: Cost equation)\newlineB+D=25B + D = 25 pounds (Equation 22: Weight equation)\newlineWe can use these equations to solve for BB and DD.
  2. Solving for D: First, let's solve Equation 22 for one of the variables. We can solve for D in terms of B:\newlineD=25−BD = 25 - B\newlineNow we have an expression for D that we can substitute into Equation 11.
  3. Substituting into Equation 11: Substituting D=25−BD = 25 - B into Equation 11 gives us:\newline$2.00×B+$3.00×(25−B)=$68.00\$2.00 \times B + \$3.00 \times (25 - B) = \$68.00\newlineNow we can distribute the $3.00\$3.00 into the parentheses and simplify the equation.
  4. Distributing and Simplifying: After distributing we get:\newline2.00×B+75.00−3.00×B=68.002.00 \times B + 75.00 - 3.00 \times B = 68.00\newlineNow we combine like terms by subtracting 2.00×B2.00 \times B from 3.00×B3.00 \times B.
  5. Combining Like Terms: This simplifies to:\newline−1.00×B+75.00=68.00-1.00 \times B + 75.00 = 68.00\newlineNow we can isolate BB by subtracting 75.0075.00 from both sides of the equation.
  6. Isolating B: After subtracting we get:\newline−1.00×B=68.00−75.00-1.00 \times B = 68.00 - 75.00\newline−1.00×B=−7.00-1.00 \times B = -7.00\newlineNow we can solve for B by dividing both sides by −1.00-1.00.
  7. Solving for B: Dividing by −$1.00-\$1.00 gives us:\newlineB=$7.00−$1.00B = \frac{\$7.00}{-\$1.00}\newlineB=−7B = -7\newlineHowever, we cannot have a negative number of pounds of seed, so there must be a mistake in our calculations.

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