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Question

A retailer sold a tablet for 1560 dollars, earning a profit of 30% of the retailer’s cost for the tablet. What selling price would yield a profit of 45% of the tablet’s cost?

Answer Choices

A. $1680 dollars$
B. $1740 dollars$
C. $1760 dollars$
D. $1800 dollars$
E. $1900 dollars$

Steps

Explanation	Calculations	Help
$We first name an unknown to represent the retailer's cost for the tablet.$	$C = retailer’s cost for the tablet$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "sold a tablet for 1560 dollars" minus cost equals "profit of 30 percent of the retailer's cost" .$	$1560 - C = \frac{30}{100} \times C$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS2-A Click to view full details
$We isolate the cost by combining like terms on the right side.$	$1560 = C + 0.30 C = 1.30 C = \frac{130}{100} \times C$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We solve for the cost by dividing both sides by 130 and multiplying by 100.$	$C = \frac{1560 \times 100}{130}$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We simplify the fraction by cancelling common factors.$	$C = \frac{130 \times 12 \times 100}{130} = 12 \times 100 = 1200$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We translate "profit of 45 percent of the tablet's cost" into the new selling price formula.$	$New SP = C + \frac{45}{100} \times C = 1.45 \times C$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We substitute the cost into the formula and calculate the new selling price.$	$1.45 \times 1200 = 1200 + \frac{45}{100} \times 1200 = 1200 + \frac{45 \times 100 \times 12}{100} = 1200 + 45 \times 12 = 1200 + (45 \times (10 + 2)) = 1200 + 450 + 90 = 1740$	Theory & Tactics Method Card CALC2-D Click to view full details

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Final Answer

B

Question

A retailer sold a tablet for 1560 dollars, earning a profit of 30% of the retailer’s cost for the tablet. What selling price would yield a profit of 45% of the tablet’s cost?

Answer Choices

A. $1680 dollars$
B. $1740 dollars$
C. $1760 dollars$
D. $1800 dollars$
E. $1900 dollars$

Steps

Explanation	Calculations	Help
$We first name an unknown to represent the retailer's cost for the tablet.$	$C = retailer’s cost for the tablet$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "sold a tablet for 1560 dollars" minus cost equals "profit of 30 percent of the retailer's cost" .$	$1560 - C = \frac{30}{100} \times C$	Theory & Tactics Method Card TRANS1-B Click to view full details Theory & Tactics Method Card TRANS2-A Click to view full details
$We isolate the cost by combining like terms on the right side.$	$1560 = C + 0.30 C = 1.30 C = \frac{130}{100} \times C$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We solve for the cost by dividing both sides by 130 and multiplying by 100.$	$C = \frac{1560 \times 100}{130}$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We simplify the fraction by cancelling common factors.$	$C = \frac{130 \times 12 \times 100}{130} = 12 \times 100 = 1200$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We translate "profit of 45 percent of the tablet's cost" into the new selling price formula.$	$New SP = C + \frac{45}{100} \times C = 1.45 \times C$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We substitute the cost into the formula and calculate the new selling price.$	$1.45 \times 1200 = 1200 + \frac{45}{100} \times 1200 = 1200 + \frac{45 \times 100 \times 12}{100} = 1200 + 45 \times 12 = 1200 + (45 \times (10 + 2)) = 1200 + 450 + 90 = 1740$	Theory & Tactics Method Card CALC2-D Click to view full details

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Final Answer

B