3. Solving Word Problems

Mixture Problem Solving

3. Solving Word Problems

Mixture Problem Solving

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Multiple Choice

Maya needs $48 of$ sq ft of tile for a backsplash. Basic tiles cost \$9 per sq ft and designer tiles cost \$25 per sq ft. She wants the overall average cost to be $dollar sign 14$ per sq ft. How many square feet of each tile should she use?

Basic tiles $equals 18 sq of ft of$ ; Designer tiles $equals 30 sq of ft of$

Basic tiles $equals 30 sq of ft of$ ; designer tiles $equals 18 sq of ft of$

Basic tiles $equals 15 sq of ft of$ ; Designer tiles $equals 33 sq of ft of$

Basic tiles $equals 33 sq of ft of$ ; Designer tiles $equals 15 sq of ft of$

Verified step by step guidance

Define variables for the unknown quantities: let $x$ be the square feet of basic tiles and $y$ be the square feet of designer tiles Maya will use.

Write the equation for the total area of tiles needed: since Maya needs 48 square feet in total, we have $x + y = 48$.

Write the equation for the average cost per square foot: the total cost is \$9x$ for basic tiles plus $25y$ for designer tiles, and the average cost per square foot is $14$, so the equation is $\frac{9x + 25y}{48} = 14$.

Multiply both sides of the average cost equation by 48 to clear the denominator: \$9x + 25y = 14 \times 48$.

Use the system of equations $\begin{cases} x + y = 48 \\ 9x + 25y = 14 \times 48 \end{cases}$ to solve for $x$ and $y$ by substitution or elimination.

5:18m

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Struggling with Beginning & Intermediate Algebra?

Maya needs 4848\operatorname{\mathrm{\operatorname{}}}sq ft of tile for a backsplash. Basic tiles cost \$9 per sq ft and designer tiles cost \$25 per sq ft. She wants the overall average cost to be $14\$14 per sq ft. How many square feet of each tile should she use?

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Maya needs $48 of$ sq ft of tile for a backsplash. Basic tiles cost \$9 per sq ft and designer tiles cost \$25 per sq ft. She wants the overall average cost to be $dollar sign 14$ per sq ft. How many square feet of each tile should she use?