Question 692368
A fifth grader would solve the problems without equations, but let's inject some x's (and y's) into the solutions, just for algebra practice.
 
1. {{{x}}} = cost of American cheese, per pound (in $)
The cost for 2.5 pounds of American cheese at ${{{x}}} per pound is {{{2.5x}}}
IF Harry has to pay $12.25 for 2.5 pounds of American cheese, then
{{{2.5x=12.25}}} --> {{{2.5x/2.5=12.25/2.5}}} --> {{{highlight(x=4.9)}}}
For American cheese, the cost per pound is ${{{highlight(4.90)}}}
 
2. Charlie has bought {{{x}}} smoothies at $2 per smothie,
so ${{{2x}}} has been deducted from his initial $30 smoothie gift card.
His balance today is ${{{30-2x}}}
If the balance on his card today is $12,
{{{30-2x=12}}} --> {{{30-2x-30=12-30}}} --> {{{-2x=-18}}} --> {{{-2x/(-2)=-18/(-2)}}} --> {{{highlight(x=9)}}}
He has purchased {{{highlight(9)}}} smoothies with the card.
 
3. Beth uses {{{y}}} inches of leather.
David has {{{7}}} more inches of leather than Beth, so he has {{{y+7}}} inches of leather.
Their combined total is {{{y+(y+7)=2y+7}}} inches of leather.
They have a combined total of {{{77}}} inches of leather, so
{{{2y+7=77}}} --> {{{2y+7-7=77-7}}} --> {{{2y=70}}} --> {{{2y/2=70/2}}} --> {{{highlight(y=35)}}}
 
4. On a nature walk, Vikram saw {{{x}}} number of birds,
and that number is 1 less than 4/5 the number of birds that Shaya saw.
Shaya saw a total of 10 birds.
So Vikram saw {{{x=(4/5)10-1}}} --> {{{x=40/5-1}}} --> {{{x=8-1}}} --> {{{highlight(x=7)}}} 
Vikram saw {{{highlight(7)}}} birds
 
7. Julio bought a stereo that cost ${{{412))) and a CD storage case that cost {{{x}}} dollars.
The total he had to pay was ${{{412+x}}}
Since he paid the clerk ${{{500}}} in cash,
he expected to receive
${{{500-(412+x)}}} in change.
He received ${{{3}}} in change, and there was no tax, so
{{{500-(412+x)=3}}} --> {{{500-412-x=3}}} --> {{{88-x=3}}} --> {{{88-x-88=3-88}}} --> {{{-x=-85}}} --> {{{highlight(x=85)}}} 
The CD storage case cost ${{{highlight(85)}}}