A renewable energy facility operates two models of solar panels: Type P and Type Q. A tota… — GMAT

A renewable energy facility operates two models of solar panels: Type P and Type Q. A total of $100$ Type P panels and $200$ Type Q panels generate a combined total of $1,400$ kilowatt-hours (kWh) of electricity per day. If the ratio of the daily output of a single Type P panel to that of a single Type Q panel is $3 : 2$ , which of the following represents the daily energy output per panel, in kWh, for Type P and Type Q, respectively?

$6\text{ kWh/day}$ for Type P and $4\text{ kWh/day}$ for Type QAnswer
B
$4\text{ kWh/day}$ for Type P and $6\text{ kWh/day}$ for Type Q
C
$3\text{ kWh/day}$ for Type P and $2\text{ kWh/day}$ for Type Q
D
$9\text{ kWh/day}$ for Type P and $6\text{ kWh/day}$ for Type Q
E
$7\text{ kWh/day}$ for Type P and $3.5\text{ kWh/day}$ for Type Q

Answer

6\text{ kWh/day}

for Type P and

4\text{ kWh/day}

for Type Q

Expressing the rates as

r_P = 3k

and

r_Q = 2k

allows us to model total production as

100(3k) + 200(2k) = 700k = 1,400

. Solving gives

k = 2

, yielding

r_P = 6\text{ kWh/day}

and

r_Q = 4\text{ kWh/day}

, which satisfies both the

3:2

ratio and the total output constraint.

Step-by-Step Solution

Set up equations based on the ratio constraint.

Let

r_P = 3k

and

r_Q = 2k

for some positive constant

k

The given ratio of outputs

r_P : r_Q

3 : 2

Set up the total daily output equation.

100(3k) + 200(2k) = 1,400

There are

100

Type P panels and

200

Type Q panels generating

1,400\text{ kWh}

in total.

Solve for the multiplier

k

300k + 400k = 1,400 \implies 700k = 1,400 \implies k = 2

Combine like terms and divide by

700

Calculate the individual panel outputs.

Type P rate

r_P = 3(2) = 6\text{ kWh/day}

; Type Q rate

r_Q = 2(2) = 4\text{ kWh/day}

Substitute

k = 2

back into the expressions for

r_P

and

r_Q

Key Concept

Work Rates and Ratios

Estimated Time:1m 0s

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