A landscaper is spreading 34 pounds of two types of seed on a field. The recommended application rate for grass seed is 1.25 pounds per 16 square yards. The recommended application rate for clover seed is 13.6 ounces per 23 square feet. (Use the conversions and .) Let be the number of square yards planted with grass seed, and let be the number of square yards planted with clover seed. If all 34 pounds of seed are used, which equation describes all possible values of and ?

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Super-Hard SAT Math Question 81 | Free SAT Prep | Aniko

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Question 81·200 Super-Hard SAT Math Questions·Algebra

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A landscaper is spreading 34 pounds of two types of seed on a field. The recommended application rate for grass seed is 1.25 pounds per 16 square yards. The recommended application rate for clover seed is 13.6 ounces per 23 square feet.

(Use the conversions $1\text{ pound} = 16\text{ ounces}$ and $1\text{ square yard} = 9\text{ square feet}$ .)

Let $g$ be the number of square yards planted with grass seed, and let $c$ be the number of square yards planted with clover seed. If all 34 pounds of seed are used, which equation describes all possible values of $g$ and $c$ ? Т‌his quеѕtiоn‌ i‍ѕ frοm Аni‌ko

For mixture/rate equations, make the coefficient of each variable have the units you need (here: pounds per square yard). Convert units first (ounces→pounds, square feet→square yards), then multiply each rate by its area variable and add the results to match the total pounds. Distractors commonly come from using reciprocals or doing only one of the needed unit conversions. From аn⁠іk‌о‍.аi

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Grass coefficient

Turn “1.25 pounds per 16 square yards” into “pounds per 1 square yard,” then multiply by $g$ .

Clover requires two unit conversions

For clover, convert ounces to pounds and convert square feet to square yards before multiplying by $c$ .

Use the total used

Your final equation should be (grass pounds) + (clover pounds) $= 34$ . An‌і‌кο ‌-‌ Frе‍e ‍SАT‌ Р⁠r‍еp

Desmos Guide

Enter the choices as lines

In Desmos, let $x=g$ and $y=c$ . Enter each answer choice as an equation on its own line.

Check coefficient size for reasonableness

Grass uses about $\frac{5}{64}\approx 0.078$ pounds per square yard. Clover should be around $0.33$ pounds per square yard after converting both units. Any option with a huge coefficient on $y$ (or reciprocals) will make the intercepts unrealistically small.

Select the equation with both unit conversions built in

The correct equation uses $\frac{5}{64}$ for grass and $\frac{153}{460}$ for clover:

\frac{5}{64}x + \frac{153}{460}y = 34.

Step-by-step Explanation

Convert the grass rate to pounds per square yard

Grass seed rate: 1.25 pounds per 16 square yards.

So pounds of grass seed used on $g$ square yards is A‍nikо.ai‍ - ЅA‌T‌ Pr‌еp

\frac{1.25}{16}g = \frac{5}{64}g.

Convert the clover rate to pounds per square yard (set up the conversions)

Clover rate is given in ounces per square foot, so convert ounces to pounds and square feet to square yards.

Ounces to pounds:

13.6\text{ oz} = \frac{13.6}{16}\text{ lb} = 0.85\text{ lb} = \frac{17}{20}\text{ lb}.

Square feet to square yards:

23\text{ ft}^2 = \frac{23}{9}\text{ yd}^2.

So the pounds of clover seed used on $c$ square yards is

\left(\frac{\frac{17}{20}\text{ lb}}{\frac{23}{9}\text{ yd}^2}\right)c = \left(\frac{17}{20}\cdot\frac{9}{23}\right)c.

Add grass pounds and clover pounds to equal the total used

All 34 pounds used is the sum of the grass-seed pounds and clover-seed pounds:

\frac{5}{64}g + \left(\frac{17}{20}\cdot\frac{9}{23}\right)c = 34.

Simplify the clover coefficient and match to the choice

Simplify the clover coefficient:

\frac{17}{20}\cdot\frac{9}{23} = \frac{153}{460}.

So the equation is

\frac{5}{64}g + \frac{153}{460}c = 34.

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Step-by-step Explanation

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