# Thread: Word Problem Help

1. ## Word Problem Help

Can someone show me how to do this question? Thanks.

Ralph works part-time for a bike repair shop. He earns $2 for each tire he installs and$5 for each gear mechanism he assembles. Last week he did a total of 40 installations and assemblies and earned $110. How many of each type of installation did he complete? 2. Originally Posted by andi01 Can someone show me how to do this question? Thanks. Ralph works part-time for a bike repair shop. He earns$2 for each tire he installs and $5 for each gear mechanism he assembles. Last week he did a total of 40 installations and assemblies and earned$110. How many of each type of installation did he complete?
Hi andi01,

State what you know and what you don't know:

Let x = the number of tires installed

Let 40 = total number of installations

Let 40 - x = the number of gears he assembles

Let 2x = earnings on tire assemblies

Let 5(40 - x) = earnings on gear assemblies

Let 110 = total earnings

Use the last three statements to set up your equation.

2x + 5(40 - x) = 110

I think you might be able to take it from here.

3. Also andi01, if you prefer, you could use two equations and solve a system of equations to get the same results.

Let x = number of tire assemblies

Let y = number of gear assemblies

Let 40 = total assemblies

(1) x + y = 40

Let 2x = earnings on tire assemblies

Let 5y = earnings on gear assemblies

Let 110 = total earnings

(2) 2x + 5y = 110

Solve the system of equations (1) and (2).

4. Originally Posted by masters
Also andi01, if you prefer, you could use two equations and solve a system of equations to get the same results.

Let x = number of tire assemblies

Let y = number of gear assemblies

Let 40 = total assemblies

(1) x + y = 40

Let 2x = earnings on tire assemblies

Let 5y = earnings on gear assemblies

Let 110 = total earnings

(2) 2x + 5y = 110

Solve the system of equations (1) and (2).
How do you solve system of equations?

5. Originally Posted by andi01
How do you solve system of equations?
(1) x + y = 40

(2) 2x + 5y = 110
-----------------------

Multiply equation (1) by -5 to get equation (3) and then add to (2). This will eliminate the y variable.

(3) -5x - 5y = -200

(2) 2x + 5y = 110
-----------------------

-3x = -90

x = 30

Substitute this value into (1) to find y.

(1) x + y = 40

30 + y = 40

y = 10

6. Originally Posted by andi01
Can someone show me how to do this question? Thanks.

Ralph works part-time for a bike repair shop. He earns $2 for each tire he installs and$5 for each gear mechanism he assembles. Last week he did a total of 40 installations and assemblies and earned \$110. How many of each type of installation did he complete?
$
2x + 5y = 110.........\left( 1 \right)
$

$
x + y = 40.............\left( 2 \right)
$

$
\text{Multiplying }\left( \text{2} \right)\text{ by - 2 and adding to }\left( \text{1} \right)
$

$
\text{and with a bit of algebra manipulation}
$

$
\text{you get: }
$

$
y = 10\text{ and }x = 30
$