Solve the following word problems involving algebra and fractions.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the word problems:

Define the variables.
Let $w$ be the number of lavender soap bars sold.
Number of lemongrass soap bars sold = $w - 6$ .
Formulate the equation using the given information that 49 bars of lemongrass soap were sold.
$w - 6 = 49$
Solve for $w$ .
$w = 49 + 6$ $w = 55$
The shopkeeper sold $\boxed{55 \text{ bars of lavender soap}}$ .
Define the variables.
Amount of apple juice = $2\frac{1}{4}$ litres.
Amount of orange juice = $d$ litres.
Total fruit punch = 5 litres.
Formulate the equation.
$2\frac{1}{4} + d = 5$
Convert the mixed number to an improper fraction.
$2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$
Substitute the fraction into the equation.
$\frac{9}{4} + d = 5$
Solve for $d$ .
$d = 5 - \frac{9}{4}$ $d = \frac{5 \times 4}{4} - \frac{9}{4}$ $d = \frac{20}{4} - \frac{9}{4}$ $d = \frac{11}{4}$
Convert the improper fraction back to a mixed number.
$d = 2\frac{3}{4}$
Mr Henderson made $\boxed{2\frac{3}{4} \text{ litres of orange juice}}$ .
Define the variables.
Let $p$ be the number of pencils Nick has.
Number of pens Nick has = $p + 3$ .
Total number of pencils and pens = 11.
Formulate the equation.
$p + (p + 3) = 11$
Simplify the equation.
$2p + 3 = 11$
Solve for $p$ .
$2p = 11 - 3$ $2p = 8$ $p = \frac{8}{2}$ $p = 4$
Nick has $\boxed{4 \text{ pencils}}$ .

Answer