A word problem can be drawn as a diagram and then translated into an equation for easier solving.
First, draw a diagram of the problem
Amount of money that Greg started with: xx
Translate the problem into an equation with the help of the diagram above
He spent a quarter of his money then half of the remainder
which is
$50$50 in total
14x+38x14x+38x
==
$50$50
Solve for xx
14x+38x14x+38x
==
$50$50
(14x+38x)(14x+38x)×8×8
==
5050×8×8
Multiply 88 to both sides
2x+3x2x+3x
==
400400
5x5x
==
400400
5x5x÷5÷5
==
400400÷5÷5
Divide both sides by 55
xx
==
$80$80
$80$80
Question 3 of 5
3. Question
A special concrete mix is made by mixing 33 tonnes (tons) of sand with 44 tonnes (tons) of cement. Per tonne, the cement costs $180$180 more than the sand. The total cost is $1392$1392. What is the cost of each component?
A word problem can be drawn as a diagram and then translated into an equation for easier solving.
First, draw a diagram of the problem
Cost of the sand per ton: xx
Cost of the cement per ton: x+180x+180
Translate the problem into an equation with the help of the diagram above
33tons(x)+4(x)+4tons(x+180)(x+180)
==
$1392$1392
Solve for xx
33tons(x)+4(x)+4tons(x+180)(x+180)
==
$1392$1392
3x+4x+7203x+4x+720
==
13921392
7x+7207x+720
==
13921392
7x+7207x+720-720−720
==
13921392-720−720
Subtract 720720 from both sides
7x7x
==
672672
7x7x÷7÷7
==
672672÷7÷7
Divide both sides by 77
xx
==
$96$96
cost of sand per ton
Solve for x+180x+180
x+180x+180
==
96+18096+180
Substitute xx
==
$276$276
cost of cement per ton
Finally, compute for the total cost of each component
Remember that there are 33 tons of sand and 44 tons of cement
Sand:
3($96)3($96)
==
$288$288
cost of 33 tons sand
Cement:
4($276)4($276)
==
$1104$1104
cost of 44 tons cement
Sand: $288$288
Cement: $1104$1104
Question 4 of 5
4. Question
A tyre manufacturer wants to create a special mix of 22 rubber types. Hard rubber is priced at $7.25$7.25/kg and soft rubber is priced at $11$11/kg. How many kilograms of soft rubber should be mixed with 88kg of hard rubber to sell for $9$9 per kg?
A word problem can be drawn as a diagram and then translated into an equation for easier solving.
First, draw a diagram of the problem
kilos of soft rubber: xx
total kilos of the mix: x+8x+8
Translate the problem into an equation with the help of the diagram above
11(x)+7.25(8)11(x)+7.25(8)
==
9(x+8)9(x+8)
Solve for xx
11(x)+7.25(8)11(x)+7.25(8)
==
9(x+8)9(x+8)
11x+5811x+58
==
9x+729x+72
11x+5811x+58-9x−9x
==
9x+729x+72-9x−9x
Subtract 9x9x from both sides
2x+582x+58
==
7272
2x+582x+58-58−58
==
7272-58−58
Subtract 5858 from both sides
2x2x
==
1414
2x2x÷2÷2
==
1414÷2÷2
Divide both sides by 22
xx
==
77kg
77kg
Question 5 of 5
5. Question
A special candy bar contains 30%30% chocolate. Another candy bar contains 70%70% chocolate. When melted together, how much of each candy bar should be used to make a 100100g candy bar that contains 35%35% chocolate?