A supplier sells 2(1)/(4) pounds of mulch for every 1(1)/(3) pounds of gravel. The supplier sells 172 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell? The supplier sells ◻ pounds of mulch and ◻ pounds of gravel.

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Convert to Improper Fractions: Convert the mixed fractions to improper fractions to simplify calculations. 2(1/4) pounds of mulch is equivalent to (2*4 + 1)/4 = 9/4 pounds of mulch. 1(1/3) pounds of gravel is equivalent to (1*3 + 1)/3 = 4/3 pounds of gravel.Set Up Ratio: Set up the ratio of mulch to gravel using the improper fractions. The ratio of mulch to gravel is 9/4 to 4/3.Find Common Denominator: Find the common denominator to combine the ratio into a single fraction that represents the total weight of mulch and gravel sold per unit. The common denominator for 4 and 3 is 12. Multiply the numerators by the necessary factors to get the equivalent fractions with a denominator of 12. For mulch: (9/4) * (3/3) = 27/12 For gravel: (4/3) * (4/4) = 16/12Add Fractions: Add the fractions representing mulch and gravel to find the total weight per unit. Total weight per unit = (27/12) + (16/12) = 43/12Calculate Number of Units: Calculate the number of units sold by dividing the total weight sold by the weight per unit. Total weight sold = 172 pounds Weight per unit = 43/12 pounds Number of units = Total weight sold / Weight per unit = 172 / (43/12)Perform Division: Perform the division to find the number of units. Number of units = 172 * (12/43) = (172 * 12) / 43 = 2064 / 43 = 48Calculate Mulch Sold: Calculate the amount of mulch sold by multiplying the number of units by the weight of mulch per unit. Amount of mulch = Number of units * Weight of mulch per unit = 48 * (9/4)Perform Multiplication for Mulch: Perform the multiplication to find the amount of mulch sold. Amount of mulch = 48 * (9/4) = (48 * 9) / 4 = 432 / 4 = 108 poundsCalculate Gravel Sold: Calculate the amount of gravel sold by multiplying the number of units by the weight of gravel per unit. Amount of gravel = Number of units * Weight of gravel per unit = 48 * (4/3)Perform Multiplication for Gravel: Perform the multiplication to find the amount of gravel sold. Amount of gravel = 48 * (4/3) = (48 * 4) / 3 = 192 / 3 = 64 pounds

A supplier sells $2 \frac{1}{4}$ pounds of mulch for every $1 \frac{1}{3}$ pounds of gravel. The supplier sells $172$ pounds of mulch and gravel combined. How many pounds of each item does the supplier sell? $\newline$ The supplier sells $\square$ pounds of mulch and $\square$ pounds of gravel.

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