Juan buys peaches and grapefruit at the store. He writes the equations shown to model the relationship between the number of pounds of peaches,

p + g = 2.5

1.58p + 1.09g = 3.46

What is the total number of pounds of peaches and grapefruit that Juan buys?

*p*, and the number of pounds of grapefruit,*g*, that he buys.p + g = 2.5

1.58p + 1.09g = 3.46

What is the total number of pounds of peaches and grapefruit that Juan buys?

-1.58p - 1.58g = -3.95 {multiplied first equation by -1.58}

1.58p + 1.09g = 3.46 {second equation stays the same}

-------------------------------

-0.49g = -0.49 {added the two equations together}

g = 1 {divided each side by -0.49}

p + g = 2.5 {first original equation}

p + 1 = 2.5 {substituted 1, in for g, into first original equation}

-1 -1

p = 1.5 {subtracted 1 from each side}

1.5 pounds of peaches

1 pound of grapefruit

=

**p + g = 2.5****1.58p + 1.09g = 3.46**-1.58p - 1.58g = -3.95 {multiplied first equation by -1.58}

1.58p + 1.09g = 3.46 {second equation stays the same}

-------------------------------

-0.49g = -0.49 {added the two equations together}

g = 1 {divided each side by -0.49}

p + g = 2.5 {first original equation}

p + 1 = 2.5 {substituted 1, in for g, into first original equation}

-1 -1

p = 1.5 {subtracted 1 from each side}

1.5 pounds of peaches

1 pound of grapefruit

=

**2.5 pounds of peaches and grapefruit****- Algebra House**