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there are $3$ cars that in total weigh $4.178$ tonnes. Car $A$ weighs $145 \, \text{kgs}$ more then car $B$ , and car $C$ weighs $260\,\text{kgs}$ less then car $B$ . How much does car $B$ weigh in tonnes?

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Add and subtract decimals: word problems

Full solution

Q. there are

3

cars that in total weigh

4.178

tonnes. Car

A

weighs

145 \, \text{kgs}

more then car

B

, and car

C

weighs

260\,\text{kgs}

less then car

B

. How much does car

B

weigh in tonnes?

Convert to kilograms: Convert the total weight of the $3$ cars into kilograms to match the units of the individual car weights. $\newline$ $1$ tonne $= 1000$ kilograms, so $4.178$ tonnes $= 4.178 \times 1000$ kilograms. $\newline$ Calculation: $4.178 \times 1000 = 4178$ kilograms.
Define car weights: Let the weight of car B be $x$ kilograms. According to the problem, car A weighs $x + 145$ kilograms and car C weighs $x - 260$ kilograms.
Write total weight equation: Write an equation that represents the total weight of the $3$ cars. $\newline$ Expression: $x$ (car B) + $(x + 145)$ (car A) + $(x - 260)$ (car C) = $4178$ kilograms.
Simplify and solve: Simplify the equation and solve for $x$ . $\newline$ Calculation: $x + x + 145 + x - 260 = 4178$ $\newline$ $3x - 115 = 4178$ $\newline$ $3x = 4178 + 115$ $\newline$ $3x = 4293$ $\newline$ $x = \frac{4293}{3}$ $\newline$ $x = 1431$ kilograms.
Convert to tonnes: Convert the weight of car B from kilograms to tonnes. $\newline$ Calculation: $1431$ kilograms $/$ $1000$ = $1.431$ tonnes.

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