Question 1178653

An athletic director buys footballs, soccer balls, and softballs for their team.

{{{x}}} > football
{{{y}}} > soccer ball
{{{z }}}> softball

- Each football is {{{4}}} times as much as each softball
=> {{{x=4z}}}......eq.1

- Each soccer ball is {{{10}}} dollars more than each football
{{{y=x+10}}} ....substitute {{{x}}}
{{{y=4z+10}}} .........eq.2

if {{{10}}} footballs, {{{10}}} soccer balls, and {{{20}}} softballs total to a cost of {{{700}}} dollars, we have

{{{10x+10y+20z=700}}}......substitute {{{x}}} and {{{y}}} from eq.1 and eq.2

{{{10*4z+10(4z+10)+20z=700}}}..........solve for {{{z}}}
{{{40z+40z+100+20z=700}}}
{{{100z=700-100}}}
{{{100z=600}}}
{{{z=6}}}

go to
x=4z......eq.1, substitute z
{{{x=4*6}}}
{{{x=24}}}

go to

{{{y=4z+10}}} .........eq.2,substitute {{{z}}}
{{{y=4*6+10}}}
{{{y=34}}}

 each soccer ball cost {{{34}}}  dollars