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Simultaneous Equations Word Problems 2Simultaneous Equations Word Problems 2
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Question 1 of 5
1. Question
What are the values of the pronumerals `x` and `y`?
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`x=` (45)`cm``y=` (35)`cm`
Hint
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First, write the simultaneous equations being represented in the problem.`5``x``+2``y` `=` `295` 
Length`3``x``+4``y` `=` `275` 
WidthMultiply equation `1` by `2``(5``x``+2``y``)``xx2` `=` `295``xx2` `10``x``+4``y` `=` `590` Subtract equation `2` from the transformed equation.`10``x``+4``y` `=` `590` `3``x``+4``y` `=` `275` `7x` `=` `315` `x` `=` `45 cm` Divide both sides by `7` Solve for `y`.`3``x``+4``y` `=` `275` `3``(45)``+4``y` `=` `275` Substitute `x=45` `135+4y``-135` `=` `275``-135` Subtract `135` from both sides `4y` `=` `140` Divide both sides by `4` `y` `=` `35 cm` `x =45 cm`, `y=35 cm` -
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Question 2 of 5
2. Question
Find the value of the base angles
- `\text(Base Angle) =` (70)`°`
Hint
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First, recall that the base angles of an isosceles triangle are equalEquate the values of the base angles and simplify`3x-17` `=` `x+y` `3x-17` `-x` `=` `x+y` `-x` Subtract `x` from both sides `2x-17` `+17` `=` `y` `+17` Add `17` to both sides `2x` `-y` `=` `y+17` `-y` Subtract `y` from both sides `2x-y` `=` `17` Next, recall that interior angles of a triangle is equal to `180°`Equate the values of the interior angles to `180°` and simplify`3x-17+x+y+40` `=` `180` `4x+y+23` `=` `180` Combine like terms `4x+y+23` `-23` `=` `180` `-23` Subtract `23` from both sides `4x+y` `=` `157` Subtract `y` from both sides Next, write the simultaneous equations being represented in the problem.`2``x``-``y` `=` `17` First equation`4``x``+``y` `=` `157` Second equationAdd the two equations.`2``x``-``y` `=` `17` `4``x``+``y` `=` `157` `6x` `=` `174` `x` `=` `29` Divide both sides by `6` Solve for `y`.`2``x``-``y` `=` `17` `2``(29)``-``y` `=` `17` Substitute `x=29` `58-y` `-58` `=` `17` `-58` Subtract `58` from both sides `-y``times(-1)` `=` `-41``times(-1)` Multiply both sides by `-1` `y` `=` `41` Finally, substitute the values of `x` and `y` to get the value of the base angles.First equation`x``+``y` `=` `29``+``41` Substitute known values `=` `70°` Second equation`3``x``-17` `=` `3``(29)``-17` Substitute known values `=` `87-17` `=` `70°` `70°` -
Question 3 of 5
3. Question
A stack of `37` coins consisting of `10` cents and `50` cents adds up to `$9.70`. How many `10` cent and `50` cent coins are there?-
`10 \text(cents)=` (22)`50 \text(cents)=` (15)
Hint
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First, let `x` be the number of `10` cents coins and `y` be the number of `50` cents coinsUse these values to create a simultaneous equations`50``x``+50``y` `=` `970` Total value of coins`x``+``y` `=` `37` Number of coinsMultiply equation `2` by `10``(``x``+``y``)``xx10` `=` `37``xx10` `10``x``+10``y` `=` `370` Subtract the transformed equation from the first equation.`10``x``+50``y` `=` `970` `10``x``+10``y` `=` `370` `40y` `=` `600` `y` `=` `15` Divide both sides by `40` Solve for `x`.`x``+``y` `=` `37` `x``+``15` `=` `37` Substitute `y=15` `x+15` `-15` `=` `37` `-15` Subtract `15` from both sides `x` `=` `22` `x =22`, `y=15` -
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Question 4 of 5
4. Question
Jason is three times as old as his son Peter. The sum of their ages is `64`. What are their ages?-
Peter's age `=` (16)Jason's age `=` (48)
Hint
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First, let variables to represent the age of Peter and Jason.`x=` Peter’s age`y=` Jason’s ageNext, write the simultaneous equations being represented in the problem.`y` `=` `3``x` Jason is three times as old as Peter.`x``+``y` `=` `64` The sum of their ages is `64`Substitute Equation `1` into `2` and solve for Peter’s age `(x)`.`x``+``y` `=` `64` `x``+``3x` `=` `64` `y=3x` `4x` `=` `64` `x` `=` `16` Divide both sides by `4` Solve for Jason’s age `(y)`.`y` `=` `3``x` `y` `=` `3``(16)` Substitute `x=16` `y` `=` `48` Simplify Peter’s age is `16` while Jason is `48` years old. -
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Question 5 of 5
5. Question
Find the value of `x` and `y`
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`x=` (20)`°``y=` (30)`°`
Hint
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First, recall that supplementary angles are equal to `180°`Equate the values of the two lower angles to `180°` and simplify`3x+2y+3x` `=` `180` `6x+2y` `=` `180` Combine like terms Next, recall that alternate angles are equalEquate the alternate angles and simplify`2y` `=` `3x` Next, write the simultaneous equations being represented in the problem.`6``x``+2``y` `=` `180` First equation`2``y` `=` `3``x` Second equationSubstitute the value of `2y` into Equation `1` and solve for `x`.`6``x``+2``y` `=` `180` `6``x``+``3x` `=` `180` `2y=3x` `9x` `=` `180` `x` `=` `20°` Divide both sides by `9` Solve for `y`.`2``y` `=` `3``x` `2``y` `=` `3``(20)` Substitute `x=20` `2y``divide2` `=` `60``divide2` Divide both sides by `2` `y` `=` `30°` `x =20°`, `y=30°` -
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