$18
Given:
Question:
How much gas money will you spend on gas each week?
This is properly a simple multiplication problem that however has to pay attention to the units carefully.
Let's find out how many gallons we need to drive over 150 miles.
[tex]\boxed{ \ = 150 \ miles \times \frac{1 \ gallon}{25 \ miles} \ }[/tex]
Units of miles crossed out.
[tex]\boxed{ \ = 150 \times \frac{1 \ gallon}{25} \ }[/tex]
[tex]\boxed{ \ = \frac{150}{25} \ gallon \ }[/tex]
Therefore, we need 6 gallons to drive over 150 miles.
And now let's calculate how much gas money will be spent each week.
[tex]\boxed{ \ = 6 \ gallons \times \frac{\$ 3}{1 \ gallon} \ }[/tex]
Units of gallon crossed out.
[tex]\boxed{ \ = 6 \times \$ 3 \ }[/tex]
[tex]\boxed{ \ = $ 18 \ }[/tex]
Hence, we will spend $18 on gas each week.
If it's already straightforward in understanding, then we can arrange multiplication operations at once.
[tex]\boxed{ \ = 150 \ miles \times \frac{1 \ gallon}{25 \ miles} \times \frac{\$3}{1 \ gallon} \ }[/tex]
[tex]\boxed{ \ = \frac{150}{25} \times \$3 \ }[/tex]
150 and 25 can be divided by 25.
[tex]\boxed{ \ = 6 \times \$3 \ }[/tex]
Once again, we will spend $18 on gas each week.
Keywords: each week, you drive 150 miles, car, 25 miles to the gallon, gas prices are $3, per gallon, how much, money will you spend, multiplication, the units
The amount of money spent on gas each week is [tex]\fbox{\begin\\\ \bf \$18\\\end{minispace}}[/tex]
Further explanation:
As given in the question [tex]150[/tex] miles of distance is covered by the car each week.
To cover a distance of [tex]25[/tex] miles, [tex]1[/tex] gallon of gas is required for the car and the price for the gas is [tex]\$3[/tex] per gallon.
The objective is to determine the amount of money spent on gas each week.
It is given that to travel [tex]25[/tex] miles, [tex]1[/tex] gallon of gas is required so, for [tex]1[/tex] mile of distance [tex]\left(\frac{1}{25}\right)^{th}[/tex] gallon of gas is required.
This implies that in [tex]\left(\frac{1}{25}\right)^{th}[/tex] gallon of gas the car runs for [tex]1[/tex] mile of distance.
Now if in [tex]\left(\frac{1}{25}\right)^{th}[/tex] gallon of gas [tex]1[/tex] mile of distance is covered so, for [tex]150[/tex] miles of distance the amount of fuel required is calculated as follows:
[tex]\fbox{\begin\\\ \dfrac{1}{25}\times 150=6\\\end{minispace}}[/tex]
From the above calculation it is concluded that with [tex]6][/tex] gallon of gas [tex]150[/tex] miles of distance is covered.
The price for the gas is $3 per gallon so, the price of 6 gallon of gas is calculated as follows:
[tex]\fbox{\begin\\\ 6\times 3=18\\\end{minispace}}[/tex]
From the above calculation it is concluded that the cost of [tex]6[/tex] gallon of gas is [tex]\$18[/tex].
Therefore, the amount of money spent on the gas each week is [tex]\fbox{\begin\\\ \bf \$18\\\end{minispace}}[/tex].
Summary:
[tex]25\ \text{miles}\rightarrow1\ \text{gallon}\\1\ \text{mile}\rightarrow(\frac{1}{25})^{th}\ \text{gallon}\\150\ \text{miles}\rightarrow(\frac{1}{25}\times 150)=6\ \text{gallons}\\1\ \text{gallon}\rightarrow\$3\\6\ \text{gallons}\rightarrow\fbox{\begin\\\ \bf \$18\\\end{minispace}}[/tex]
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Simplification
Keywords: Simplification, multiplication, miles, distance, price, gas, $3, each week, drives 150 miles, money spent each week, 25 miles per gallon.
