Maya needs $48$ 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

Let the number of square feet of basic tiles be represented by $x$ and the number of square feet of designer tiles be represented by $y$.

Since Maya needs a total of 48 square feet of tile, write the equation for the total area: $x + y = 48$.

The cost per square foot for basic tiles is $9$ and for designer tiles is $25$. The overall average cost per square foot is $14$. Write the cost equation based on the weighted average: $9x + 25y = 14 \times 48$.

Use the first equation $x + y = 48$ to express $y$ in terms of $x$: $y = 48 - x$.

Substitute $y = 48 - x$ into the cost equation and solve for $x$: $9x + 25(48 - x) = 14 \times 48$. After finding $x$, substitute back to find $y$.

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Maya needs 4848 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 $48$ 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?