+87 E-Z Stop Fast Gas sold $10,957 worth of gasoline yesterday. Regular sold for $2.30 a gallon, and premium sold for $2.55 a gallon. If the station sold 420 more gallons of regular than of premium:
a. How many gallons of each type of gasoline were sold?
Do not enter units in your answer.
Premium: gallons
Regular: gallons
b. If the profit on regular gas is $0.18 per gallon and on premium is $0.20 per gallon, what was the station's total profit?
$
+122 Let x be the gallons of premium. This means the regular gallons will be x + 420. Add these together to the total profit.
$${\mathtt{2.3}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{420}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{10\,957}}$$
$${\mathtt{2.3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{966}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{10\,957}}$$
Now factor out the x
$${\mathtt{x}}{\mathtt{\,\times\,}}\left({\mathtt{2.3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{966}} = {\mathtt{10\,957}}$$
Now solve for x.
$${\mathtt{4.85}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{9\,991}}$$
$${\mathtt{x}} = {\mathtt{2\,060}}$$
a)
2060 gallons of premium,
2480 gallons of regular.
b)
Profit for premium: .20 * 2060 = $412
Profit for regular: .18 * 2480 = $446.40
Total profit: $412 + $446.40 = $858.40
+122 Let x be the gallons of premium. This means the regular gallons will be x + 420. Add these together to the total profit.
$${\mathtt{2.3}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{420}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{10\,957}}$$
$${\mathtt{2.3}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{966}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{10\,957}}$$
Now factor out the x
$${\mathtt{x}}{\mathtt{\,\times\,}}\left({\mathtt{2.3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2.55}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{966}} = {\mathtt{10\,957}}$$
Now solve for x.
$${\mathtt{4.85}}{\mathtt{\,\times\,}}{\mathtt{x}} = {\mathtt{9\,991}}$$
$${\mathtt{x}} = {\mathtt{2\,060}}$$
a)
2060 gallons of premium,
2480 gallons of regular.
b)
Profit for premium: .20 * 2060 = $412
Profit for regular: .18 * 2480 = $446.40
Total profit: $412 + $446.40 = $858.40
